No, sodium methoxide and t-butyl bromide cannot be used effectively for the preparation of t-butyl methyl ether. This is because t-butyl bromide is a tertiary halide, which undergoes elimination rather than substitution with a strong base like sodium methoxide. It leads to the formation of alkenes via E2 mechanism.
Instead, methyl bromide (CH\textsubscript{3}Br) and sodium t-butoxide should be used. Since CH\textsubscript{3}Br is a primary halide, it undergoes SN2 reaction easily with t-butoxide ion, forming t-butyl methyl ether.