Firat time lagering and in a state of panic.

I tried my hand at making a lager yesterday.
I tossed in the yeast before putting into carboys but due to being not informed enough I put the carboys instantly in my fridge (luckily only around 50 F degrees) but later find out that you want it to sit out for 24 hours to get the yeast started up before refrigerating.
It was in the fridge for about 3 hours before I took it out to sit. The room temp is 65 F and it’s been 10 hours since sitting out and i am not seeing any signs of fermentation.
Did i screw it up due to refregarating so quickly?

No.  You did not screw it up by putting wort into a 50F fridge.  What yeast strain did you use?  What was the temp of the wort when you pitched the yeast?  Some of my early screw ups were from pitching yeast into wort that hadn’t cooled sufficiently.  Bringing your yeast up to temp before pitching is a common practice which may help in speeding up the beginning of fermentation but not necessary.  Just listened to a Brulosophy podcast with a woman from Imperial Yeast who recommends keeping yeast at 34F until time to pitch unless making a starter.

No need to panic. It will almost certainly be fine.

Depending on the yeast strain, lag time can be a nerve racking experience.

I agree with the earlier posts.  Most people get a cleaner fermentation when they pitch into cold wort rather than pitching warm and cooling it down to fermentation temps.

RDWHAHB