Can you, yes.
In regards to time and effectiveness, there is no way products alone and scrub brushes can compete with a steamer or extractor.
You can however, get good results, none the less.
There are some great products out there that can really attack and remove stains and dirt.
You will have to do your research.
Also look into kitchen chemistry approaches.,
You will need various scrub brushes, scrub pads, and magic erasers.
Don't forget quality microfiber towels that can really pick up dirt.
In regards to equipment, you by no means need to spend a fortune.
My steamer, wet/dry shop vac, and Little Green Machine cost me a total of $200.
I use these machines for heavy duty work, and nothing has failed me yet.
Products are very important in regards to interiors.
This due to various types of interior stains.
Protein, Tannin, Ink, Oil and Grease, etc....
You will need to spend the money to get a dedicated cleaner for each type of stain.
Then, a general cleaner for everything as well.
Good luck, keep us posted.