You were told six months. Six months is a sales answer. The honest answer is that different fixes pay back on completely different timescales, and knowing which is which is the whole skill.
Removing a noindex tag, fixing a wrong canonical, unblocking a path in robots.txt. These are permission problems, and once permission is granted the page can be back within a crawl cycle, sometimes the same week.
A new page gets found, stored, and given a provisional position. Then it moves as real people click it or do not. The first number you see is not the answer, and reacting to week one is how good pages get deleted.
Whether a site is trusted for a subject builds over quarters, from other people linking and from a body of pages that consistently answer one kind of question. There is no shortcut here that is not also a risk.
Positions bounce daily and mean little. Impressions for terms you did not previously appear for is the earliest honest signal that something worked, and it usually shows up long before traffic does.
This is teaching material and our own reading of standard practice, not advice for your specific site. Check anything important with your own specialist.
Run the free check, then tell us what it found. We reply with what to fix first and why. No call, no pitch.
If a word here is unfamiliar it is defined in the SEO glossary. Two public penalties and one problem we found on our own network are pulled apart in the case studies, and the longer pieces live in the library.