Usually these issues are caused by the cabling system, although a bent derailleur hanger can be the cause (so check first if your rear derailleur hanger is bent before throwing any money at new cables).
Also check if your dear derailleur is correctly adjusted -- the cable tension and both limits screws need to be correctly set, but if the problem happens only on the biggest cogs (lowest gear), it means only the cable tension and "L" limit screw can be the culprit as the "H" limit screw only activates on smallest cogs (biggest gear).
Checklist for cable issues:
- Is the outer cable something other than Shimano SIS-SP41 / OT-SP41? Off brand cables should be replaced.
- Is the inner wire something other than Shimano stainless steel inner wire (or if you want better shifting performance in the current ridiculous finely spaced gear counts, Optislick or perhaps polymer coated but some say the polymer coating tends to get damaged over time so perhaps Optislick would have better longevity)? Non stainless cables should be replaced as they can rust.
- Are the outer or inner cables old? Even the best quality cables can get damaged as they are used, and also can get damaged over time even with no use with exposure to changing weather, so many years old cabling systems could require replacement.
- If the inner cable runs below the bottom bracket exposed, is the area where the cable runs dirty or clean? It should be cleaned if dirty.
- Are the cables correctly routed? The bends should be as gradual as possible and there should be no wrong direction bends. The cables should be as short as possible without violating these rules. See the four commandments of cable routing.
- Has the initial cable slack been removed? After installing cables, you need to pull the inner wire hard away from the frame in the highest (hardest) gear, to ensure the cable housings become correctly seated. If you are using a trigger shifter or some other type of shifter with fragile parts, you need to limit the force of pulling the inner wire. If you are using thumb or bar-end or downtube shifters, you can pull very hard, no need to limit the force. On a new expensive bicycle, this probably has already been done, but on a cheap bicycle the manufacturer may have omitted it, thinking that the housings become seated on their own with use. However, this doesn't happen always quickly and reliably.
Failing that, I would ensure the rear derailleur pivots work well without any friction and drop a bit of oil on the pivots. However, the more likely culprit is the cabling system.
Also it could be the case the components are not even supposed to shift properly. For example, the lowest end components such as Tourney are just junk. You can't make such junk work well.