I have seen 始まる constructed with から several times. Yet, the start is a point in time, not a period. For instance, I would expect
～から始まる are possible; it's just that they emphasize different things.
Xに始まる emphasizes the precise time that something begins, with the focus being on that specific point. The particle に pinpoints that exact moment as a temporal identifier of the stated event X.
Xから始まる emphasizes the fact that there is a span of time which started from a certain point X but continues forward. If differs from the above in that it includes a recognition that there is a starting point X as well as a period of time which follows that can also be considered contiguous to the start point and relevant.
I could point out that this is possible in English too:
(1) School term starts on April 1st.
(2) School term starts from April 1st.
These are both possible but as with the Japanese sentences, they have a slightly different focus, Sentence (1) emphasizes a specific point and Sentence (2) includes the span of time which follows from that point.
In either English or Japanese, which one you decide to use depends on what you want to express in your sentence.