There are studies that show TSH does rise with age, so it is not certain that you need medication.
Whether or not you need medication depends on whether you have symptoms of hypothyroidism that are bothering you.
It is important to note that hypothyroidism is not jut inadequate thyroid hormone, but instead, it is best defined as inadequate T3 effect in tissue throughout the body due to insufficient supply of, or response to, thyroid hormone. T3 is the biologically active thyroid hormone, so this TISSUE T3 EFFECT determines your thyroid status. Also there are many variables that affect your body's RESPONSE to thyroid hormone. TSH has only a weak correlation with the thyroid hormones Free T4 and Free T3, and a negligible correlation with TISSUE T3 EFFECT. Free T4 and Free T3 have only weak correlations with TISSUE T3 EFFECT. In fact there are no reliable direct measures of your thyroid status. The best way to try and assess a perso's thyroid status is to start with a full medical history to see if there are potential causes for a thyroid problem. Next should be an evaluation for symptoms that occur more frequently with hypothyroidism. Along with those, a number of tests should be done: Free T4, Free T3, TSH ( and if high, then TPO ab and TG ab), cortisol, Vitamin D, B12 and ferritin.
So before further discussion, please tell us about all symptoms you have. It might help make sure you don't overlook any symptoms by using the following link from another site. Just review and then tell us all symptoms you seem to have. Note that if you use or take something to avoid a symptom then you have the symptom, such as using skin moisturizer is a sign of dry skin.
There have been studies of the effectiveness of thyroid hormone therapy for older adults who had not previously taken thyroid hormones. But I think those studies are somewhat flawed.
However there was a very interesting and relevant fact reported in one of those studies published in 2017. For their study, they screened for participants over 65 years old with elevated TSH (4.6 to 19.9). They found that 60% of participants that initially screened for entry into the study on the basis of elevated TSH were found to have normal TSH in subsequent testing, and were therefore excluded from the study. That is, their TSH returned to normal without any treatment. The authors also stated that this phenomena had been found in other studies.
Now to your question: can you wait a while. Again, a key factor would be if you are having any sort of health problems. I would ask when you got these test done and do you have previous tests with similar results. If you are feeling fine and this was the first time for thyroid tests, I would say it would be prudent to wait a while and get the tests done again (2 - 3 months??). If you go this route, make sure that you insist that your doctor orders all the thyroid tests again.
If you are interested in reading about that 2017 study, I give the link below. However it could be daunting if you are new to thyroid matters. And it could also lead you astray if you only read their one line conclusion: "Levothyroxine provided no apparent benefits in older persons with subclinical hypothyroidism." That conclusion is a sweeping generalization of their results and ignores a number of important limitations of the study that the authors list near the end of the report.
Thyroid Hormone Therapy for Older Adults with Subclinical Hypothyroidism, June 29, 2017, N Engl J Med 2017; 376:2534-2544
Due to the lack of correlation to TISSUE T3 EFFECT that I mentioned, a TSH test is useful for diagnosis of thyroid status only when it is at extreme levels. Your TSH is slightly above range, your FT4 is at very bottom of its range, your FT3 is only about 17% of its range and your TPO ab is near the range limit. All together it may indicate early stages of Hashimoto's Thyroiditis that has not yet resulted in hypothyroid symptoms. I am strong believer in the old saying, "If it ain't broke, don't fix it". So I agree with telus2 that waiting and monitoring how you are feeling would be a good idea, along with getting re-tested in a few months.
Your labs show subclinical hypothyroidism. This may or may not cause symptoms. But to add, you might have symptoms and not realise it. For instance, my hair thickened up on thyroxine to my surprise. You could trial a low dose of thyroxine to see if you feel any improvement. Give it at least 6 weeks.
As suggested previously, I would not want to start on thyroid med before actually noticing symptoms. When you do start, I would consider asking for a desiccated type med that contains both T4 and T3. I say this because most people find when taking T4 only, their very important, FT3 level lags well behind FT4 level due to inadequate conversion of T4 to T3. This prevents adequate TISSUE T3 EFFECT.
What I would do to be proactive, is to find out if your doctor is willing to prescribe T3 type meds. Even more important is to find out if the doctor is willing to treat clinically, by adjusting Free T4 and Free T3 levels as needed to relieve hypothyroid symptoms, rather than just based on TSH levels. Also need to find out if doctor is willing to test for cortisol, Vitamin D, B12 and ferritin. If either answer is no, then you will need to find a good thyroid doctor that will do so.
The desiccated med I mentioned would include NatureThroid, NP Thyroid and Armour Thyroid. Each grain of these ( 65 or 60 mg, depending on the brand) contains 38 mcg of T4 and 9 mcg of T3.
If you will give us your location, perhaps we can suggest a doctor that has been recommended by other thyroid patients.
I'd like to add a few more comments. If you talk to people taking thyroid hormones (TH), I think 99% of them would probably say that they wish they weren't. Some doctors think it's real easy, but it isn't easy to get back to normal. Which for you means that you should make every effort possible to avoid having to start taking them. When we said earlier that it may be prudent to wait and see about taking TH, we should have added that does not mean that you shouldn't do anything. While your lab tests show that your TH might be slightly low, your thyroid is still producing a goodly amount of TH and there are things that you can do to protect and support your thyroid. This is where your doctor should have started, rather than writing a prescription for Levothyroxine (T4).
First, the two most common causes of thyroid problems are Hashimoto's and Graves disease. They are both autoimmune diseases. There are many articles and books written about autoimmune diseases and the thyroid gland. You must do research and then examine your lifestyle and nutrition to see if there is anything that could contribute to autoimmune disease and if so correct it.
Second, there are many nutritional factors (e.g. vitamins and minerals, etc) involved in the normal functioning of your thyroid gland. A simple example is iodine. Iodine is required to produce TH; is there enough in your diet or supplements? Again, you must research this and see if you might have any deficiencies.
You will do yourself a huge, huge favor if you do these two things and avoid taking TH.
Last, I'll add some comments about Armour, also known as natural desiccated thyroid (NDT). Your doctor suggested that you take 25 mcg of T4. That is a little bit of T4, considering that a normal dose is around 100 to 125 mcg. I don't want to sound too melodramatic, but I would say playing around with a little bit of NDT is like playing around with a little bit of dynamite. Lots of people take NDT, but you have to know what you are doing, and there are too many doctors who do not know the first thing about it because they were never trained to use it.
I will try to explain where the problem could arise. Your doctor, in suggesting 25 mg T4, recognizes (I hope) that it would be additive to the TH that your thyroid is producing, that is, the total TH available in your body would be 25 mcg plus the amount that your thyroid makes. Taking a small amount of NDT might do the same thing. But when you get up to a certain amount of NDT, it has the characteristic of making your TSH go very low, and that "turns-off" production of TH from your thyroid gland.
Let's look at a hypothetical example. A normal person's thyroid produces about 95 mcg T4 daily. Let's guess that your thyroid is at 80% efficiency and making 76 mcg T4. Now suppose you take 1.5 grains (60 mg) of NDT, which contains 57 mcg T4 and 13.5 mcg T3. This amount of NDT is typically enough to make your TSH go very low (this is believed to happen because of the fast acting T3 it contains). If your TSH goes very low your thyroid will stop making the 76 mcg T4. So you will have gone from 76 mcg T4 in your body to having only the 57 mcg from the NDT. At this point you will assuredly be hypothyroid and have symptoms.
Because of this characteristic of NDT, patients usually have to take a full replacement dose, rather than a little bit. But if you have a doctor who does not understand this, simply looks at your low TSH and says I'm not going to give you anymore, well you've got a problem.
You have a lot to consider and I hope you can follow this.