A backlink only helps your rankings once Google's crawler has found and indexed the page it's on. Until then, it's invisible to your rankings, no matter how good the placement looks.
Why some backlinks never get indexed
A few common causes: the hosting page itself isn't indexed (low-authority or brand-new sites can sit in Google's crawl queue for weeks), the page has a noindex tag, the site has crawl budget issues from excessive low-value pages, or the link sits on a page Google has deprioritized due to thin or duplicate content.
How to check if your backlinks are indexed
Search site: plus the exact URL of the page hosting your link in Google. If it doesn't appear, it's not indexed. Ahrefs and similar tools also flag indexation status directly in backlink reports.
What a proper campaign should do about it
Monitor every placement and resubmit or replace anything that fails to index within a reasonable window. This is a standard part of any legitimate link building service, and if an agency doesn't mention indexation checking as part of delivery, ask directly whether they track it.
A few things worth clarifying
Anywhere from a few days to several weeks, depending on the hosting site's crawl frequency and authority.
Submitting the URL via Google Search Console's URL Inspection tool can help, though it's not guaranteed.
It passes no SEO value. A reputable provider should replace it at no extra cost.