Hand planes probably need more finessing before use than any other tool in the shop. Take the time to tune one properly before launching into your good wood, and you’ll be so much happier with your work. It just takes a minute and eliminates so much frustration.
Sharpen the blade first and set the cap iron just back from the edge by about 1/64 to 1/32″. Reassemble the plane and check the blade first to see how far it’s sticking out of the body. I very gently rub my fingertip against the blade to feel for this. Adjust the depth of cut for a normal sized shaving of about .002″. The dollar bill in your pocket is .004″, so thinner than that piece of paper. You say your finger isn’t calibrated for this? Of course not. Just get the depth of cut close for now and you’ll fine tune it later. Just know that you won’t have to push the plane so hard, work as hard on your board, or sharpen as much if you take thinner passes with your iron.
Then put a piece of scrap wood on edge in the vice. Take a cut on the edge with the plane first on one side of the blade and then on the other. Compare the shaving sizes and adjust the blade with the lateral adjusting lever so the cuts are consistent in thickness all the way across. Adjust the depth of cut again to make sure the shavings are thin enough and then and only then can you launch into the satisfying work of planing your wood.