How long does it take for a new website to get indexed by Google?

Yes, that is normal. A brand-new site with no backlinks can take anywhere from a few days to several weeks before Google indexes more than the homepage.

To speed it up:

1. Add the site to Google Search Console and submit your XML sitemap.
2. Make sure no page has a noindex tag and that robots.txt is not blocking anything important.
3. Link your main pages from the homepage and menu so crawlers find them quickly.
4. Request indexing for your 5–10 most important pages (there is a small daily limit).
5. Earn a few links from real, relevant sites. Links are how Google discovers and trusts new sites.

You can build a clean sitemap and check your robots.txt with the free tools on SEO Stack Hub.