There is a product called a finish pen. It is like a stain pen that is loaded with polyurethane instead of stain.

You will need to sweep a hardwood a few times a week. Vacuuming is allowed so long as you turn off the beater bar.

Photos of the floor would be helpful.

That's ridiculous. My floors (white oak, factory finish, Bruce brand, I believe) are over 17 years old and look like new. Two adults, and the beater brush on the vacuum cannot be turned off (it's the one thing Consumer Reports didn't like about his vacuum while rating it very highly many years ago).

I too feel that it is ridiculous that these floors look this bad in so short a time.

Photos please. Factory finishes are often "Aluminum Oxide" urethane finishes. These finishes have a tendency to scratch "white". This is particularly annoying when the colour is medium toned or darker.

Aluminum Oxide is put down in layers (layer of urethane with a powdering of AO and then baked). These layers can "separate" which then appears as a "scratch". These fine white lines LOOK like scratches but don't FEEL like them. It can be quite puzzling.

If these are Aluminum Oxide "white" scratches, then the finish pen isn't going to help. The permanent markers would be the best option.

Photos will help us determine what type of damage/scratches you have.