Suspension is nothing new to gravel. Even going as far back as 2006, Ted King won Unbound using a Cannondale Slate, a 650b gravel bike with a Lefty suspension fork. Rockshox, Cane Creek ...
The best gravel bikes under $1,000 in the US or £1,000 in the UK will let you get started gravel riding without too much expense. At this price point, you'll usually find an alloy frame.