How long after moving a fridge should you wait until plugging it in?

I purchased a used fridge yesterday. I was really busy so I didnt have time to do any research before actually attempting to pick it up. Now I have read through several websites on the does & donts. The fridge was to large for us to transport vertically so we layed it on its back. (which now I read isn’t such a good idea) The drive was only about 5–10 minutes to my house. Once unloaded the fridge sat upright for a good 45 minutes before we plugged it in. Once connected it seemed to start up and everything lit up as it should. This morning I went to get a water I had left in there last night to find that it wasn’t cooling. Is this normal? I read on one site that sometimes it can take a few days before it starts cooling properly especially if it has been turned off for a while. I dont know if I should be worried we damaged it in transit or what could be the problem?