On e.g. a Giant Stance, can the lowest gear on the cassette be upgraded to a higher tooth count just by only changing that cog?
It seems the Giant Stance is equipped with Shimano Alivio. That's a fairly low-end groupset and I'm fairly sure you can't replace the cogs one-by-one. In any case, a whole new cassette is only about $20–25.
You might be able to separate the individual cogs. This can be done by grinding off the small rivets that hold a subset (typicaly three of the larger cogs) of the cassette together. The rivets don't do anything except make it difficult for you to maintain your cassette by replacing individual cogs, something Shimano probably doesn't want because they make less money. But it's better for you. I have CS-6500 9 speed cassette with custom 13-15-17-19-21-24-27-30-34 gears. You can't buy it like this but you can make it yourself and it's a great way to go. I replace only the worn individual cogs when needed. When the cassette is taken off for cleaning, which I always do when replacing a chain, the cogs and spacers fall off one by one. I return them one-by-one onto the spindle and replace a worn cog if there is one. This is the best way of doing it. Shimano don't want you to do this because it's good for you and bad for them.