Instead of just pressing in, try pumping on the clutch pedal. Does 2 or 3 pumps first make it work better? If so, you could possibly get by for a short time by doing that, until you get the hydraulics fixed. My 20+ year old Corolla has had this problem twice over the course of its lifetime, and replacing the clutch master cylinder fixed it straight-away both times. For most car’s that’s a simple and relatively inexpensive repair.
If you are hoping the problem will go away, unlikely. It will almost certainly get worse. To the point where you won’t be able to shift at all. And you know that’s going to happen when you are 75 miles from home on a cold snowy winter night. So best to get this addressed with due speed.