One diagnosis decides it: fix content and intent-fit if the page under-serves what page-one results deliver, and build links and authority if the page already matches intent as well as page one but lacks the trust to break through. The two levers solve two different problems, so pulling the wrong one wastes effort. The job before choosing is to figure out which problem you actually have, because a page stuck on page two is stuck for one of these reasons, not both equally.
The pivot is under-serves versus matches-but-stuck. To run it, pull the live page-one results and compare your page honestly against them. If the winners answer the query more completely, fit the intent more precisely, or cover sub-questions yours skips, then your page under-serves and content is the lever: close the gap first, because no amount of links will rank a page that answers the query worse than the competition. If your page matches page one on intent and depth and simply sits below it, the missing piece is trust, and links and authority are the lever, because the page has earned relevance but not yet the credibility to pass established competitors.
The default reflex is to assume links break every plateau, and that is exactly the trap. Pointing links at a page that under-serves its query props up a weaker answer and rarely holds, because Google is comparing the content and yours still falls short. Equally, pouring more content onto a page that already matches page one does not address a trust gap and can dilute a focused answer. The lever has to match the diagnosis, which is why you diagnose before you choose.
So compare your page’s intent-fit and completeness against page one first. If you find a real content or intent gap, close it before anything else. If you find your page already matches and is simply outranked, shift to earning links and authority. Diagnose, then pick the one lever the diagnosis points to.