Is it possible that plant life (or rather, alien plant analogues) could start as seaweed in water, before evolving to become terrestrial, similarly to what happened with animals and fungi? And if so, what would the environment have to be like for this to happen?
Given time and mutations and a food supply, any X can evolve to a Y if you wish. It's a question of how difficult and improbable it is. Generally, it's plausible over billions of years (the span of an alien biosphere's development) if there's a "path" of adaptations where each will over some benefit over the previous. (And you're allowed to have later parts of the path overwrite earlier ones, not that we'll need that here.)
For this case, in more detail: We can suppose that your original "seaweed" lives in shallower water, and adapts to the low salt concentrations of rivers. Following that, some parts of some riverbeds will occasionally dry out in less rainy periods. Those seaweeds that happen to have better water retention will survive those events more often ... etc. Gradually, the seaweeds at the edges are those which require only need to be immersed to move seeds about. The seeds are winnowed down to those resilient to being left high-and-dry, until they can be left for a full year between floods, or even carried by other means (wind?). At that point, seeds which can handle drier conditions will be the only ones to survive there, giving them unchallenged access to a patch of sunlight. This lets them grow in peace, and produce as many seeds as possible ... some of which have "horrible mutations" that happen to help them survive in harsher conditions. And so it goes. Thicker cell walls might be a stupid waste of time in the sea, but support large leaves on land. Some mutations would be fatal in the water, but don't matter on land.
Oh look, we not have a mutated seaweed which can't live in the sea. Let's call it ... a weed. Or maybe a plant, to be polite.
And just for the sake of it, let's put it in orbit around a blue-tinted star and have it photosynthesise with something marginally more reflective in the lower-energy visible light range. Now it looks reddish, and we have a War of the Worlds reference.