You need memory proportional to the number of nodes you visit (score of the node, previous node on the shortes path to this node, list of next candidates). There is nothing preventing you from creating everything else lazily, and in practise most nodes will never get visited.

A* also allows you to find a solution faster by overestimating your heuristic: For example if you multiply your heurisitic with 1.1 you are guaranteed to find a path whose length is within 10% of the shortest path, requiring less CPU time and memory for the search.