Practicing at home is a very important part of learning a new instrument, especially on the drums. You need to learn to coordinate all 4 of your limbs at the same time. The first month of lessons is set up so that you will not need to do as much home practice, but more thinking, listening and interpreting. After this if you choose to continue lessons it is highly recommended that you have some way to practice on a drum kit at home in order to get benefits out of the lessons.
I understand that it is a large investment to buy a good quality full sized drum set. So! You have options. Electric drum sets are cheaper than acoustic sets, and they are significantly less noisy. You also have the option of just buying individual pieces of a drum set, which would include: Snare Drum, Bass Drum, High-hat. There are also plenty of cheaper acoustic sets that you could start off with. If you need support or don’t know what you should be looking for, feel free to reach out and I can give you some suggestions!