

A push-pull BJT configuration seems like it could be appropriate, if your application will be unbothered by limiting the Vgs to a max of 5.5v (the 3224’s max supply voltage). The MOSFET in question seems to be good for Rds(on) below 20 mOhm at that voltage, so it seems fine for at least a handful of amps.
If you are doing higher frequency switching than a few kHz, then you probably want to use a driver IC. And especially so if you have a higher voltage bus than the 5v needed by the ATTiny.




I suppose it’s worth mentioning that the 3224 datasheet suggests that it’s perfectly capable of running at 3.7 volts directly, since it has a wide voltage range from 1.8v to 5.5v absolute. But I imagine you have other ICs that need the 5v supply.
I’m not entirely familiar with what you mean by a “convertor”, but I presume it’s some sort DC to AC function. Given the output loading, 3 amps through that Toshiba MOSFET seems reasonable enough, with the power dissipation being something like 0.3-0.5 W max, depending on switching speed.