Generally, but not always, with a 3x7 hybrid and running in the middle chainring you can run all 7 cogs without getting chain rub on the front derailleur cage. Worst case you can get 6 of the 7 cogs.
Hybrids typically run trigger shifters or twist shifters. Older ones also had thumb shifters. Thumb or twist shifters are friction and you can trim the front derailleur slightly to eliminate chain rub. You can't trim trigger shifters.
Regardless of the type of shifters, you should make adjustments to the front derailleur setup to eliminate as much of the chain rub as possible. This will probably help...
https://www.parktool.com/en-us/blog/...eur-adjustment
John