Powering transformers using a switching transistor circuit on DC instead of AC
Yes. In fact most MODERN power supplies use that principle. That is called "Switch-Mode Power Supply" (SMPS).  It is almost required by law in new electronic equipment (including phone chargers, etc.) for efficiency greatly exceeding the old-style big "heavy-iron" transformers that ran at electric mains frequencies (50Hz and 60Hz).  SMPS typically operate at 10s or 100s of KHz and use a much smaller ferrite transformer for equivalent power as the old-school "heavy iron".