The amount of space in the game world is incredible. So it should be possible to find a remote corner away from others, of course you would be far away from any trade hub, getting that far would mean building a colony ship while you are still in the starting area. Of course it gets easier if building a small station means a small render distance. The developers have mentioned that players can build safe zones around stations, the details are not clear but if a solo player can do this and removing a player built safe zone is difficult, then a large player faction might intentionally ignore stations that are small and distant. Of course nobody has had a chance to really test if solo play via hiding is possible, and that could change depending on how many move out across the system, and how zealously big factions attack the little guy.
https://wiki.starbasegame.com/index.php/Space
I have to push back against XenoCow. It is likely that playing the game entirely out of your ship will be impossible, the size difference between ships and stations, and even the name of the game, suggests that you will need certain Station-only equipment to survive on your own. Surviving on your own will also require access to resources, which means being relatively close to the belt or a moon, though considering the scale of everything 100 km away is still close enough. Ultimately Frozenbyte does need to make accommodations for solo players and small companies who want to avoid large factions.