As others have mentioned, 45 days is too short to see any significant results. However, last year I had a site that saw a boost just one week after the backlinks were indexed. Notice I said indexed, not built. This leads me to some important points that only a few people have touched on:
Are you sure the links are indexed? If they're not indexed by Google, you won't see any results now or even in 1000 years. Manually check each backlink in Google to see if it's there. If you have hundreds of links to check, use software like Scrapebox to track your SEO efforts. Despite its steep learning curve, it's invaluable for serious SEOs.
Are you sure the links you purchased are D0F0LL0W? Many newbies, myself included in the past, often forget to ask sellers if the links are d0f0ll0w or nofollow. This is crucial because links with the 'nofollow' tag won't pass any link juice, authority, DR, DA, or any other benefits. They’re essentially useless.
Are the links still live? Believe it or not, some unscrupulous sellers remove the links 1-6 months after payment. It's possible that some or all of your links have been deleted, which is detrimental since Google won’t see or index them. If Google doesn't index your links, they won’t help your site rank. This is another area where Scrapebox is invaluable, as it can track the status of your backlinks, including their indexation, d0f0ll0w/nofollow status, and whether they are live, dead, or broken.
If all three previous points are checked off, then seriously, give it some time. Many links, especially weaker ones, can take months to index nowadays. You can expedite the process by asking the seller to index them for you, either for free or for a fee, depending on your package or negotiation skills. Alternatively, if the links are guest posts or niche edits on high-quality websites, ask the site owners or editors if they’re okay with you using an indexing service or blasting your guest posts/niche edits with thousands of low-quality links to help index your main links. Some owners may be fine with this, while others may not be.
And again, wait! I can't give an exact timeframe, but probably 4-6 weeks after building the links and submitting them to indexers. If your links are still not indexed by Google after 6 weeks, then it might be time to take more aggressive measures.