If you are referring to the recent published FIPS 203 and FIPS 204 standards which specify ML-KEM and ML-DSA respectively (both are Module Learning with Error primitives, which are a particular variety of LWE system), then the options are very limited.
No, $q=2^t$ is not a permitted parameterisation. In fact for ML-KEM the only permissible value is $q=3329$ and for ML-DSA the only permissible value is $q=8380417$.