I started from the same point like you (strapless wave before).
My first (strapless) foil setup was a Moses W633 / 91 cm mast and a "Skate" board from Groove Kiteboards (120 cm length, 5 cm thick, dunno about width any more).
That was pretty easy to start with, and also suitable for wave foiling.
Recently I changed the board to an Anton "Skater", 100 cm long and only 1.5 cm thick, super light (1.8 kg), super robust. This is much more fun to ride than the bigger board, particularly in waves. You could use it even as a beginner due to its large scoop (nose of boards bends upwards). Touchdowns are very foregiving.
https://anton-kiteboards.de/produkt/ant ... -skater-2/ (hand-made 100 % in Germany by one of the most experienced shapers, really good quality, very fair price)
Just like kamikuza says: Volume mainly enhances the light-wind properties of your foil setup. But as a beginner, light-wind is not what you want (as it makes everything much more complicated). Hence I´d say: Thick boards are not essential for a beginner.
It took me a long time to get into waves (hip-high maximum yet) with a foil. You need a lot of practice to gain the confidence needed. On a foil, even rediculessly small waves get over-exiting! But this is an essential part of the fun!