Are ranged weapons assumed to be unloaded until the Attack action or is it possible (within the rules) to enter a fight with a loaded weapon?
Yes, but ask your DM
Certainly there is no rule saying the action of loading must be done immediately before attacking, however depending on the level of realism applied to the game, this could be dangerous.
An unloaded crossbow cannot misfire and in real life a crossbow left loaded will break down pretty quickly. Your DM may allow it with these risks applied.
However DnD is not real life and has no weapon durability mechanic, and this certainly would not be a game breaking allowance and certainly falls within the rules so yes, you can preload a crossbow