For all employees, don't just hire people permanently, even if you or someone else
thinks they're a great fit, "try before you buy". Definitely work with someone on a temporary contract basis, and renew it,
before hiring, even a first employee, and then don't re-up a contract if they don't work out. If they need benefits, that's cool, you probably should be taking care of people.
Next time, check out their portfolio at the phone-screen step, because each designer's tastes and abilities vary widely from individual to individual. Run it by enough people on the "search commit" (which might be just be founders and another couple folks) for input, because you need buy-in to dispel any appearance of 'PHB CEO is arbitrarily hiring people without due-diligencing them and foisting them on us'.
Because each hard fire makes the the hiring manager and other interviewers look bad, and it hurts the candidate... trial run (without abusing that indefinitely) and be nice & professional should be the HR-focused mindset.
If you absolutely have to fire someone, do it now, do it yourself... It's a bandaid that's gotta come off, because putting it off just wastes your time and theirs, when they can be elsewhere possibly improving and someone else with a better fit could get going sooner. Be direct, honest and talk about next steps. Give feedback if they can take it and possibly help them if it, as long as doesn't put you into any HR/legal hot-water. Perhaps it's "We've discussed it and determined we have an irreconcilable mismatch in terms of design quality and taste. We're bummed that we're gonna have to let you go."
Also, have someone else impartial (before you get an HR manager) do an exit interview to see if they're going to bad mouth you, if they have useful feedback or if they're anything your shop can do to help them transition elsewhere.