It usually depends on how long you have to keep the deposit before using.  Yes the accounting practice is to book it to a liability account

But you can just create a credit invoice at 3-2 to That debits cash as your deposit. Then after your first T&M billing apply the deposit through cash receipts and include a statement showing the balance due.

Note:  The T&M invoice is not a statement and therefore not going to show cash applied. 

It usually depends on how long you have to keep the deposit before using.  Yes the accounting practice is to book it to a liability account

But you can just create a credit invoice at 3-2 to That debits cash as your deposit. Then after your first T&M billing apply the deposit through cash receipts and include a statement showing the balance due.

Note:  The T&M invoice is not a statement and therefore not going to show cash applied. 

Thank you for this answer!  I was hoping there would be an easy way as we immediately start using the deposit.