Your deposit creates an equal asset and liability on the bank's balance sheet remember assets = liability + equity must balance.

Deposits are liabilities to the bank's customers. The cash the bank has, regardless of how it got it, is an asset. The cash may result from a customer making a deposit, but its still just cash. Deposits and cash are separate items on the balance sheet. Here is an example from the Fed:

https://www.federalreserve.gov/releases/h8/current/

Note that cash is a single line item. The banks could get that from other sources, such as loan repayments.