I think I did 3k for the exact purpose OP is mentioning (extra points on the card I use). I also pay it off at the end of the month. I have done this with other car dealers. Normally 3-4 or even 5k is ok depending on how you word it to the "car dealer". Tesla might or might not be different, but with a regular car dealer you, you never "ask" what you can put down. You "tell" them what you want to do.
Again, with other dealers, you say something like:
"By the way, I will need to put 4k of this on this credit card to make this work for my finances... otherwise I need to postpone buying this car" They always take it.
Now, with tesla its different, but I put 2.5k on my credit card down, and then another 1k when I picked up I think.
I need to correct myself here a bit. The advice is still good, but I checked my records to see if I was correct in remembering that I put down an additional 1k on my credit card at delivery of the tesla like I said I did above.
I mis remembered this. I DID do this for my wifes 2019 X3, which we got 3 weeks after getting the tesla, but for the Model 3, I put down the 2500 deposit on the credit card, and then a check for a large amount for a down payment, and a bank check from my credit union to finance a smaller amount. I intended to buy a mid range model outright, but test drove a performance and basically said "shut up and take my money" at that point, so financed the difference in cost between a mid range outright and the performance I bought, at Dec 2018 Model 3 performance prices (lol).