Is it permissible to browse the search page on Instagram – which displays objectionable content before a search term is entered – aimlessly, for entertainment, or to look for good pages?

There is no harm in browsing those pages for a permissible purpose. The presence of objectionable content does not matter if one turns away from it and does not look at it. Therefore, a person must lower their gaze from objectionable things and not persist in looking at them.