We know that fundamental particles (Quarks, electrons, etc.) were formed a while after the Big Bang. How was their electrical charge (its value and sign) determined? Was electrical charge present in the pre-Big Bang singularity and then distributed between particles, or the electrical charge was itself formed after the Big Bang? If the latter, how was the electrical charge produced? How was it assigned to different particles?
Charge and energy-momentum are both locally conserved in general relativity. Cosmological solutions don't extend to the singularity at $t=0$, they only cover $t>0$. According to GR, charge and energy-momentum have been locally conserved at all times $t>0$. GR doesn't say anything about how this connects to a time $t\le 0$, because according to these models, there is no $t \le0$.
Note that charged particles can be formed in charge-conserving reactions, as long as the total final charge equals the initial charge. This isn't a GR issue, it's true in flat spacetime as well. For instance, charged particles are produced from a zero-charge initial state in beta decay of a neutron, or in pair production.