Is it normal to have irritated eyes the first time you put in contact lenses?

It happens. Irritation is not "normal", but can result from the eye being unused to having a foreign body (the contact lens) in it! Dry eye can make irritation more likely as can overwear during the initial period of use. Redness is a "red flag"! don't continue to wear the lenses without first checking with your eye are provider!
Absolutely. The cornea is a tissue that has no blood vessels, but like every other tissue in the body, it needs oxygen. When you put a contact lens on the eye, it has to get used to a change in which oxygen is delivered to the cornea. The eye becomes pink/red due to the change in oxygenation. With time, tolerance to the lens builds up and the redness and grittiness disappear.

Related Questions

Is it normal to have red/irritated eyes the first time you put on the contact lenses?

Sometimes. Red eyes sometimes happens the first few times you wear your lens due to rough handling of the lens with beginners. This will get better. Ask your eye doctor for assistance if you need and good luck!

Irritated eyes with contact lenses. What relieves them?

Finding problem. Treating the symptoms will not provide a permanent solution. You have to find out the problem's cause. Perhaps the eye is dry, or the contact is too tight or one of several other possibilities. See your eye doctor if you wish to continue successful contact lens wear.