The game is supposed to be a bit slow at the beginning, and if you run out of money early on, I recommend restarting the game or deleting your save file.
Clarifications:
The game isn't about passing days quickly.
The game is about meeting people and trying to host them by talking to them. If you try to advance the days quickly to try to get money, it will only make things more complicated, since the more days that pass without attending to the characters, the more opportunities you lose, and negative events can happen quickly.
Things are somewhat expensive because they aren't necessary at the beginning, since you wouldn't be able to host so many people with so few resources.
One tactic is to try talking to several people, find a 3-star or lower character that you like, buy a lot of persuasion items, and try everything with them when you see them at the door. Try everything in one go.
Additional ways to earn money include using shop codes, which are not mandatory; they are just a bonus and not the game's main source of currency. You can claim items there and sell them from your inventory for a cash boost, but this strategy isn't required.
Another way to earn money is by completing exploration missions, such as the Christmas exploration mission or tactical mode.
There is NSFW content, but the game is more about meeting people, trying to understand them, hosting them, managing things, and doing NSFW activities.
The NSFW rooms are just a bonus and fanservice.
Hard-looking, muscular men require patience ;3