The verb is describing the start, which is neuter. I think. (I'm tiiiiired today...)
было was (neuter)
начало the start, the beginning - notice, it's neuter, this is the word that is "using" the verb - the verb is describing this noun, not месяц
месяца of the month, because it's in the genitive, the начало "belongs to" the month.
If I was asking when did the month start, I might say something like когда начался месяц? The verb would then be describing the noun month, and therefore would need to be in the masculine form.
HTH, and hopefully a native/non-ridiculously-exhausted person will correct anything I explained badly or got wrong ;-p