In my experience, you will be able to submit the initial rentista application before having the bank account -- and you'll need to, since you'll need to bring the precaria to the bank to have any hope of opening an account.
Getting a bank account without a DNI, though technically legal, is a challenge. Banks are apparently not required to give you one, just allowed to give you one (according to the manager of my branch). You do have to get an account and start showing transfers before you get the DNI, though. I was able to get an dual account at Santander by escalating the issue to the branch manager and arguing repeatedly that the bank and Migraciones had conflicting rules with circular logic. He said they would close my account after 90 days if I didn't bring a DNI by then, but so far they haven't. By default it was a dual dollar/peso account, and I was able to receive dollars via Swift and then extract them as USD cash.
Our attorney advised us that the rules on this are changing, so I believe the new rules are that it has to be transferred in USD via Swift transfer. Previously you could transfer the correct peso amount through Western Union to your bank account. Essentially the amount per month has doubled.