Read the coastline first, not the outline
An outline gives you two very different kinds of edge, and only one of them is natural. A coastline is drawn by the sea and is irregular at every scale — bays, capes, estuaries, islands. A land border is drawn by people, and people draw straight lines. That distinction does most of the work.
So the first question is not "what country is this" but "what kind of shape is this": an island, an archipelago, a peninsula, a long coastal strip, or something with no sea at all. Each answer removes most of the world. Only about a fifth of countries are landlocked, and they cluster — central Africa, central Asia, central Europe, the interior of South America.
Then look for the single most unusual feature and trust it. One sharp cape, one deep inlet, one improbably straight border running for hundreds of kilometres. Countries are much easier to tell apart by their exceptions than by their overall proportions, which is also why a half-remembered shape is often enough.