Not sure about your temperatures exactly, (as a person from Europe)
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I have grown those Begonias twice, and as they are tender perennials, not frost resistent, I alsways treated them like my Dahlias.
, keeping them indoors as long as the nights are very cold, and plant them outside when the weather turns warm/mild, always worked for me. Grew them on the balcony, they started flowering later than bigger, bought plants.
When i was still at school, i did an intership for three weeks at the communal nursery/ city nursery, in February. I remember that they startet those Begonia bulbs that early in a heated greenhouse because they grow somewhat slower than Dahlias. Well, just my two cents or something, a good summer, bye, Lin