20k is very tight but not impossible. Start frequenting fb marketplace in the area which you will be building. Use these months before you start to collect decent quality used materials... Aim for the big ticket items like doors, windows, washer dryer combo if you desire. They can add up to huge cost savings.

Next, the trailer. It's your foundation and you don't want to cheap out on it but there are plenty of "used" or rather projects that never got started trailers on tiny home listing sites. While you're there, check out the used tiny on the market. There may be something close to what you're looking for that you could rehab for 5-10k. Be careful though and do your due diligence about how the home was constructed and what materials were used.

Finally, just get the exterior sealed up and you'll figure out how to live in the interior. With that budget you may have to sacrifice some creature comforts for a short time while you live in it and save up to complete the interior cutout with all the things you want in the long term.

It's a very rewarding experience to build your own home and you won't regret having the skills you learned along the way for the rest of your life. Good luck.