Sap flow in trees is a result of sap pressure accumulated in the roots during a frost, which is then released when the temperature thaws during the day. Many tree species cannot be harvested because they do not develop high enough sap pressure to bleed (according to Venerable Trees, Inc.).
One farm in BC reports that birch sap is harvested just after maple:
Birch trees begin to run sap about the time the maple trees are
finished. Before the buds swell up and burst into leaves – usually
when the nights are still below freezing but the daytime temperatures
are above freezing – end of February to the middle of March in BC or
even into the first part of April, depending on the year.
This is consistent with the average min/max monthly temperatures for Quesnel, BC:
Interestingly, Cornell University gives the same temperature conditions for maple trees as described above for birch, i.e. when day/night temperatures swing across the freezing point. I'd suppose birch trees just prefer a bit more warmth.
In particular, the University of Alaska Fairbanks says birch prefers a daytime temperature consistently above 50 °F. This occurs about mid-April in that region, but earlier for Quesnel as per the graph above.