If, when mentioning handsize increases, we restrict any and all forms of draw, building an engine becomes difficult, but there are some cases where it’s possible. For starters, you usually need all your estates and coppers trashed - if you can’t draw through them, an engine would be far too unreliable. Provided this, there’s a few cards that can definitely play through your deck with a massive payload to boot, even without any draw.
Economy cantrips are the obvious example - a deck of highways and markets is one of the simplest 8+ province megaturn engines you can set up. Minions are also good at this. While they don’t conventionally increase handsize, you can play them for virtual money, discard 1-0 cards, then end up with a fresh, albeit smaller hand of 4 new cards. There’s also Vassal and Herald - cards that don’t increase handsize on their own, but let you play cards from the top of your deck to get around the limitations of a 5 card hand.
If you’re being lax about the ‘no draw rule’, you can simulate a minion deck with economy building engine pieces and ‘draw to X’ cards. Play 3 squires for actions, nomad camp, jack of all trades, draw back up to 5 cards with $5 and 2 buys. There’s also a few niche cases - rebuild can work with a draw-less engine (if we’re counting rebuild as an engine here), and a whole bunch of groundskeepers along with a couple buys/gainers can let you rapidly gain estates or duchies at the value of provinces or colonies to make up for a more limited payload.
In short, there are definitely options out there. They aren’t guaranteed, and access to draw almost always improves an engine’s potential, but there’s still options.