The honest answer: it depends, and anyone who gives you a date for page 1 is guessing. Google's own advice on hiring an SEO says no one can guarantee a #1 ranking on Google (Search Central, "Do you need an SEO?"). Here's what is actually known.
What Google Says About Timing
Google has to find a page before it can show it. Google says crawling can take anywhere from a few days to a few weeks, and that asking it to crawl a page doesn't guarantee the page will be included in results (Search Central, "Ask Google to recrawl your URLs").
Once a page is in, where it shows up depends on the search, the competition, your Business Profile, your reviews and more. Google doesn't publish a timeline for that part, and neither should anyone selling you SEO.
What We Tell Our Own Clients
New pages usually start showing in Google within weeks 3–6. That's showing up, not ranking first.
Leads tend to follow your Google Maps listing, so your Business Profile and your reviews matter as much as the pages. We don't promise a ranking or a number of leads. Our monthly report shows you what actually came in.
What Affects the Timeline
Competition. A specific search in a smaller town, like "epoxy flooring Clinton Township," is usually easier than a broad one in a big city, like "roofing Detroit."
Your starting point. If you already have a site Google knows about, keep its addresses working when you rebuild: redirect every old page to its new home, so you don't throw away what's already there.
Your Business Profile and reviews. For local searches the map results come from Business Profiles. A verified, complete profile and a steady flow of reviews are things you can start on today.
Real pages. A page for each service and each town you really work, each one genuinely useful, gives Google something worth showing.
What to Do While You Wait
Ask for a review after every job. Keep your Business Profile up to date with new photos and accurate hours. Check Google Search Console to see which searches your pages are starting to show up for, and build on those.
The key is patience paired with steady work. Get the site built right, keep the profile and reviews moving, and give it time.