From my past experience (last year with my Model 3 order at the end of Q1, and from what I saw happen to other people during that same time), if you placed your order anytime in March then Tesla would try their best to source a car, get you to take care of your financing & paperwork right away, so they can get it delivered to you by 3/31. Last year, I re-ordered (after the factory had shutdown) another Model 3 on 3/29, and took care of the financing and everything on 3/30, and the car was set to be delivered on 3/31 - which I received via home delivery at 8:30pm at night on 3/31.
There were some people who had rejected their orders in late March and had to wait longer (into April) to get another car, but from what I saw they got their deliveries around the 2nd week of April. However, it looked like most of those cars were March builds that may had been rejected, then fixed & corrected, and finally sold to new owners. I also remember that some people still didn't get a car delivered in early April, and had to wait until mid-May when Tesla was able to build a car for them. Although back then, european & chinese Tesla cars were still be built out of Freemont so those builds took precedence before US cars during the early part of each quarter.
Things may have changed with the way Tesla is now doing things from a year ago, especially with the China factory up & running at full capacity and able to pump out cars for Europe. However, I still think if you place an order in late March or the beginning of April, that you may get one a March build that wasn't sold in Q1 (which are most likely getting built right now as of this post, or will be built in the next couple of weeks). But if you want to wait for an even newer build that's not from March, then you may be looking closer towards a late-May or June delivery before the end of Q2.