I'm not sure you could; Basic Rule "triggers" are events, not states. Turning on is an event; being on is a state (or condition). The Basic Rule would need something to "wake"/trigger it, which would necessarily be either a location or device event or a schedule (specific time, etc.). How would it know when to check? It isn't impossible theoretically; you could basically do it already with a time trigger and a restriction for a switch's state, but you can only set a single time "trigger," so it's probably a poor choice. In any case, I think the desired approach to solving this problem isn't looking at it from the right angle for this reason.
Not that this is a good idea, either; you could do a periodic schedule in Rule Machine. But you'll be triggering the rule a lot, often to do nothing. I suppose if it's mostly overnight, you may not care, but it's generally better to respond to actual events if you can (but you probably can't here if they don't report state on physical power change, as most don't).
For bulbs, you might even be able to do something better: are these Zigbee, and do the new "Advanced Zigbee..." drivers work with them? (Make sure to hit "Configure" after you switch drivers.) If so, there is an in-driver option for default power-on state there that will avoid you needed to handle this so the app level at all. Some Z-Wave bulbs also have this as a parameter you can set.