How can we trust supply won't be increased by just a few lines of code?
The bitcoin network is composed of 'bitcoin full nodes', which are computers located all around the world, each one running independently to verify the state of the network.
Part of that verification includes making sure that the right number of coins are being created with each passing block, such that the total number of coins in existence is known, and predictable.
To change this 'coin issuance schedule', you would have to change the code running on all of those computers, so that they would all independently agree on some new issuance schedule, and could all continue to verify which blocks are valid (or not), in independent consensus. If you could only change the code on some of those computers, then those computers would start to follow blocks which the remaining bitcoin network nodes would consider invalid, effectively creating an altcoin-fork of the network (similar to what happened with 'bitcoin cash').
Anybody, at any point in time, could create some software that changes the issuance schedule. Thats easy. The hard part is convincing everyone that is running a bitcoin full node to switch to this new code, which creates more coins. Nobody has the authority to push such a change onto the network (top-down governance), rather it is the independent choices of all of the network's nodes (bottom-up governance) that defines the network.
So the answer is that you don't have to trust someone to not increase the supply. You just have to run some code that will verify that they haven't.
Well, the title is the only question, how can we trust supply wont be increased by just a few lines of code?
Just don't make any such changes to your code and you will never see an increased supply. You control the code running on your computer. If you never want to see an increased supply, never change your code in that way.
You can, of course, only interoperate with people who also don't want to see an increased supply. So the real issue has nothing to do with changes in code, it has to do with wanting a guarantee that there will still be people who don't want changes in the supply for you to interoperate with.
But you cannot ever force anyone to interoperate with you if they don't want to.