You are likely limited to 10 speed as
@NorCal_In_AZ suggested. If I were in your position, I would take a look at the Microshift Advent X line. They offer 10 speed cassettes with 11-48T range, along with clutch derailleurs and compatible shifters at a very reasonable price. They also have their Advent (9 spd) and Acolyte (8 speed) drivetrains with similar derailleurs and shifters, but in a up to an 11-46T ans 12-46T respectively.
Looking at the OE Shimano Tourney TY501 crankset, you're also going to have to order a new set of cranks as the ones you have are riveted.