There are a few things you can try to help Google index your backlinks faster:
Check the status of your backlinks in Google Search Console. If the backlinks are showing as “discovered,” it means that Google is aware of them, but they have not been indexed yet. If the backlinks are not showing up in Search Console at all, it could mean that there is a problem with the backlink itself or with the website it is on.
Use the “Fetch as Google” feature in Search Console to request that Google re-crawl the pages on your website that contain the backlinks. This can help Google discover and index the backlinks more quickly.
Make sure that the pages on your website that contain the backlinks are being crawled by Google. You can check this in the “Coverage” report in Search Console. If the pages are not being crawled, it could be because they are blocked by robots.txt or because they are not linked to from other pages on your website.
Build more high-quality backlinks to your website. The more high-quality backlinks you have pointing to your website, the more likely it is that Google will discover and index them quickly.