In that case: it might be possible, but it would cost an insane amount of money. It would not surprise me one bit if the cost would exceed $100k. And it will matter little whether this is a Camry or a Honda Jazz or Protege or whatever. The problem is the insane markup on individual parts, not to mention markup by the dealer. And then you have to also pay for a space to put everything together. It the end you’ll end up with a janky version of a car which probably has a metric ton of issues, for the most outrageous amount of money.

If you really want a “new” old car, your best bet is to scoop up a low mileage version. They will be overpriced, but will still be a lot cheaper than the initial idea. I’ve seen listings of ‘80s cars with < 100 miles on them for sale. Always extremely expensive, but there are people interested in that kind of thing. Do note that a 10+ year old car that has not been used, is going to require work to get going. Rubber deteriorates, things seize when not used.

If your initial idea came from the wish to save money, just get a decent second hand one and be happy with ever year you’ll get out of it. Learn to do maintenance and you’ll keep running cost down and the car will likely even last longer.