Can we delete data using SQL job and insert data into the same table at the same time from another application

I have created one SQL job and it is executing a stored procedure to delete data from the table at a specific time. But at the same time, if anyone will try to insert a record in that same table from another application through APIs then I am getting a timeout exception for that request. Error is > Microsoft.Data.SqlClient.SqlException (0x80131904): Execution Timeout Expired. The timeout period elapsed prior to completion of the operation or the server is not responding. Can I achieve both tasks at the same time without error? Thanks in advance!