I've had a beard for most of the almost 40 years since I got out of the 'Tower.
The itchyness when it is just coming in is a result of three factors:
1. The hairs are relatively short and this means they can't flex as much as longer hairs.
2. The ends of the hairs are cut square because of your recently-stopped shaving.
3. Your skin isn't used to dealing with with the sharp edges of the growing hairs.
A shampoo with jojoba (not jejojobah - yuk yuk yuk!) oil in it will make the hair feel softer. I've used Bumble and Bumble Alojoba shampoo in the past. To be honest I don't use it regularly because once the beard is a month old it will be pretty soft. Using a conditioning rinse might also help.
One thing that I really feel is most helpful - even though this will sound weird - is to get a bar (not the liquid form) of LAVA brand hand soap and really work the bar over the beard to work up a big "mad dog" lather. LAVA hand soap contains fine pumice powder, which is abrasive enough to wear the edges of the beard hairs while your face enjoys a super-rich, smooth lather. When the cut edges of the hairs is worn a bit the hair won't itch as much. I am a BIG fan of LAVA hand soap for cleaning more than dirty, greasy hands.
(A famous internet retailer sells bars LAVA hand soap and the Alojoba shampoo.)
I'm not kidding! You can probably get it in supermarkets or hardware stores. Try a bar - if you don't like it on your beard you will be able to use it for dirty or greasy hands.