It is normal.
What is not "correct" is the phrase "one day/a few days". It is overly optimistic.
If your page was not indexed within minutes, you are on the waiting queue for manual inspection and that can take from a few hours to several weeks. It is not first in first out. If you promote your game elsewhere and get natural traffic, that might speed it up, and is a good idea in general. Also, you have payment active first time. Those tend to take longer.
Itch might avoid a lot of support inquiries and topics like this one by updating their faq with a more realistic time estimate.