In my opinion the best time to start fitness for your retirement years should start in your fifties or sixties. That’s not to say that those who exercise beginning at an early age have it wrong. Starting at any age is great.
The CDC reports that for those aging from 55-64: only 35% exercise, those aging 65-74: 31% 75 and older: 18%. The results were even worse if muscle-strengthening activity was included: 55-64: 17%, 65-74: 16%; 75+: 8%. https://www.cdc.gov/nchs/hus/contents2017.htm?search=Physical_activity/inactivity,
Sure, the reasons are obvious for decreased exercise with age, arthritic pain and increased susceptibility to injury are big ones. But our concept of exercise could conjure images of young people running 5k races, doing vigorous aerobic workouts, or lifting hundreds of pounds. In addition, what motivates people to exercise in their youth may not be as important in retirement years, (e.g. looking in shape, breaking your personal speed record). To add, middle aged and older people may prefer free or low-cost workouts, and hitting the gym may be out of the question.
So, to get around this, starting a different routine that is designed to keep you from hurting your body (in particular your joints and spine), and help you avert the nursing home, and stay healthier in general should be your new goal. Forming good habits to do this then can best be started in your mid-fifties, but again, actually can start any time.
The CDC guidelines recommend 150 minutes of moderate intensity aerobic activity weekly, such as brisk walking, or to save time, 75 minutes of vigorous activity, or a mix of each. This means about 30 minutes a day for five days, which can be done three times daily, ten minutes at a time.
Muscle strengthening activity twice a week can be done too, in as little as 5-10 minutes at a time, but no guidelines as of yet for this requirement have been set. The CDC has put out a series of free series of muscle strengthening videos you can do at home.
https://www.cdc.gov/physicalactivity/basics/videos/index.htm

Examples of muscle-strengthening activities include weight lifting, resistance bands, and completely free techniques such as calisthenics, using your own body weight for resistance (e.g. push-ups, pull-ups), shoveling, gardening, stair climbing. The idea is to involve most of the major muscle groups. With resistance training, one set of 10 repetitions is a good goal to start out.
Exercise can reduce the rate of falls, a major contributor of nursing home admissions. We’ll talk more about falls later.
The assumption is that exercise should keep you healthy and young. Is there evidence?

First, study from the National Cancer Institute presented the following data showing how any leisure activity you do can extend your life.

A MET is basically a unit of activity.

• 1 MET is your resting metabolic rate obtained while your are just sitting there.
• 3 METs: walking about 2.5 MPH
• 7 METs: jogging

So if you walk 2.5 MPH for 30 minutes a day, that gives you 3 X .5 X 7 = 10 MET-hr/wk, But the wonderful thing is that not only did you burn calories, you actually gained almost 4 years extra in your life. Not to mention that this will make you healthier in general.
And to reinforce this, people who engage in physical activity for 7 hours per week have a 40 percent lower chance of dying early than people who are active for less than 30 minutes a week.