Hello!
Sam from Moz's Help Team here!
So - after being found, newly discovered links have the ability to be populated into our index in about 3 days. However, there are a lot of factors which can affect our ability to find and index links to your site. It's important to note that we are always adding new data to our index, but it may take some time for us to discover backlinks to your site based on factors like crawlability of the referring pages, quality of the links and the referring pages, and more.
If you are not seeing links that you know you have, you may want to make sure that they can be indexed. It is also a good idea to check to see if we've indexed the page on which that link is found. If we haven't indexed the referring page yet, you won't see your link in our index.
You can also add links to Link Tracking Lists. Once you add a link to your tracking lists we will add that page to be crawled. As long as it is accessible to our crawler, you should see the link in our index as soon as we can index those pages.
Lastly, I have a great guide here with some things to check around why we may not have found your links yet: https://moz.com/help/link-explorer/link-building/moz-isnt-finding-your-links If you'd like any further information, please feel free to pop us an email over at help@moz.com. We do also have a great guide to Domain Authority just here: https://moz.com/learn/seo/domain-authority