No. Not first. Your Google Business Profile does the early work, and most local businesses ask this backwards. The question is what the first dollar should buy.
Where your buyer is
Someone needs a detailer, a caregiver, a tutor. They search, Google shows them three businesses on a map with stars next to each, and they call one. A lot of buyers do all of that without leaving Google once.
For that buyer, your Google Business Profile is your website: the photos, the reviews, the hours, the button they press. And a profile is live on the map the day it’s finished. No design project, no launch, no hosting bill.
A website you’ll build “someday” ranks exactly as well as no website.
What a website is for
None of that makes websites pointless. It makes them a second purchase. A website starts earning when:
You have more than one thing to rank for. Multiple services, multiple towns. Each wants a page, because a profile is one pin in one city.
Your buyer researches before they trust. Home care and clinics are the standing exception: a family checks the website before they call, and a missing one costs the call. (We wrote up what that website needs to say separately.)
You’re answering long questions. Pricing logic, process, before-and-afters: things a profile can’t hold.
The order of the first dollar
Profile first: complete it, activate it, answer the reviews, let it take the calls. Website when the profile is working and you can name the job the site would do: more cities, longer answers, or a trust check you’re currently failing.
That’s the order we run it in too: every plan works on your profile, and the website is a one-time build you add when it has a job. Yours to keep either way. Start with the profile →
NASP 
Wild Foods Co. 
Noble Origins 
Cowboy Pools 
BT Biltong