I've thought about it some more and to keep things simple I don't think we should include any custom logic for ensuring an initial burn amount. There are actually a lot of ways to brick the contract with an initial deposit. This current method prevents the share inflation attack, but you can also just send a non-zero balance to the contract before the first call to deposit to DoS any deposit after that as convertToShares(...) will return 0 always since psm value is > 0 and totalShares = 0.

I think instead let's just make it very clear a small seed amount should be deposited as the first action in all cases. This is what other protocols do, and I think it's easier to not go overly fancy as it introduces complexity.

For the deposit and withdraw functions let's add a receiver param and during deployment we will just deposit some initial amount and send it to the zero address.

As part of the deployment script we can include this initial deposit to force the deployer address to have a seed balance inside it's wallet.

Mostly looks good. Some requested changes.

I would also make the recommendation to burn at least 1 full unit instead of 1000 shares.

Good to merge now.