Would you let Google index an early version of a new site?

I recently launched a small new site on its real domain. The basic structure is live now, but I’m still improving the content, internal links, and page layout.

I’m trying to decide whether to let Google start indexing it now, or keep indexing controlled until the core pages are more polished.

My current thinking is mixed.

On one hand, letting Google discover the site early might help with crawling, Search Console data, and getting the domain into the index sooner.

On the other hand, I don’t want Google’s first impression to be a thin or unfinished version of the site, especially if some pages may still change.

For new small sites, do you usually let Google index the early version and improve over time, or keep things noindexed until the main content and structure are ready?