OK, so let's break this down. How does a person get to the Olympics?
First they have to get a spot on an Olympic team. Since you asked about track and field, let's consider that.
First you have to go through the "trials" for your country. When you run a sanctioned race (i.e., a real competitive race with timekeeping, not a 5K beer run or whatever) if you run it fast enough you might post a qualifying time.
http://www.usatf.org/events/2012/OlympicTrials-TF/entry/qual...
The A time is the "A"utomatic, "you're allowed to come to the trials" time. The B is the "B"ackup - we'll invite you to the trials if you are consistently hitting B times and there aren't enough A people.
If you post an A time (or enough B times), you'll be able to attend the US Olympics track and field trials. You go there and run like a mad man or woman against the best athletes in the country. If you are fast enough, congrats - you're going to the Olympics!
But how fast is "fast enough"?
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A 5K is a pretty common race, right? How fast can you do it? I'm lucky if I can do it in 30 minutes, but I'm a big blubbery programmer.
The B time for a 5K is 13:50.
Let's look at some times for 5Ks. Here's a big one with lots of finishers:
http://www.albanyrunningexchange.org/results/search.php?ID=3...
The fastest runners aren't even close.
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OK, not a 5K. Let's consider another data point. The NYC & Boston Marathons attract major talent.
http://www.runnersworld.com/races/tougher-standards-for-2016...
There aren't even B standards for men. You have to run a marathon in 2:18 to go to the trials.
http://raceday.baa.org/top-finishers.html
http://www.ingnycmarathon.org/Results.htm
The top 15 are already almost falling outside the qualifying. Do you think any of your friends can finish in the top 15 of the Boston Marathon? I know a guy who has been running all his life, who trained his ass off and ran the Boston Marathon in 2:50 a few years ago - he finished in the top one percent for the race, but that is nowhere near Olympic trial times.
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What about a nice sprint? The 800M A time is 1:46.50, and the B time is 1:48.30. Not too long, or so it seems...
http://www.tfrrs.org/results/31188_1946804.html
The best college athletes in the country aren't even automatically qualifying. But hey, ~a man and a dream~, right?
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This entire idea is beyond ludicrous. No one's going to "hack their way to the Olympics", especially a 36 year old that is nowhere near their peak physical condition & has limited experience in the sport.