I know nothing about the bike per se, but if you want to see date codes on each component, go to:

vintage-trek.com & on the left click on component date codes, and it will tell you the numbering system for component manufacturers. That way you can see what year the bike might be if the components are original to the bike. It's a starting point.

I have an '85 and an '87 Japanese bike and your Suntour AR front derailleur looks consistent with the era of your bike. Your Shimano Deore rear derailleur is a mountain derailleur and is of later vintage - like early 1990's. Maybe 1990. So betting the rear derailleur has been replaced. Your shifters appear to be Suntour also.

Look under the bottom bracket shelll or the rear dropouts for letters or numbers, indicating serial number. Post it here.

Chain rings are drilled, so look nice. What does the writing say? Something "GT"?