You've been able to tell Android to place calls by voice since time immemorial, but it has gotten a lot smarter over the years. Now, with OK Google commands, you can place a call without even touching the phone. It only makes sense you could activate the speakerphone in that situation, and indeed you can. At some point, Google added the ability to begin a call on speakerphone with only a voice command.
So here's now it works—launch the voice prompt with OK Google or by tapping the voice icon, say "call X on speakerphone," and that's it. This way you don't have to pick up the phone just to toggle on the speakerphone for a hands-free call. A card will show up with a progress bar, giving you a chance to abort before the call is placed. Speakerphone won't activate immediately when the call connects. Instead, that only happens when someone answers.
I've tried this on a few devices and it seems to work. There's some confusion about when this was added, but it's probably been at least a few weeks. As with many of Google's voice features, you'll probably need to be using US English input mode.