“For hundreds of millions of years, green algae lived in freshwater environments that periodically fell dry, such as small puddles, river beds, and trickling rocks,” said Professor Michael Melkonian, from the University of Duisburg-Essen.
http://cdn.sci-news.com/images/enlar...atophyceae.jpg
The two algae, Spirogloea muscicola and Mesotaenium endlicherianum, are close unicellular relatives of the land plants.
So, plants did not evolve from seaweed that somehow crawled onto land. They evolved from single celled algae that already lived on land in ponds and small puddles that often dried up. And when they split from their relatives 580 million years ago, like the illustration in the article shows, they were still unicellular.
The real question then is when they evolved multicellularity. Either way, judging by the fossils available so far, it wasn't before 400 million years ago of so that we got plants that were more than just knee high.