Multicellular fungi and algae, including green algae, had been around for many hundred million years by that time. As you are probably aware, the ozone layer is now getting thinner, thanks largely to human activity. It is unlikely that one alga all of a sudden became a terrestrial plant. In all likelihood, some plants acquired the ability to withstand short periods of desiccation. These may have given rise to those that were able to do so for almost all of their life cycle.
Some characteristics are critically important to plants living on land.
Several fossil plants seem to have had some of these characteristics and are, therefore, thought to have spent some or all of their life on land. Ability to withstand desiccation . Extant land plants have a cuticle and guard cells. Ability to withstand the effects of more intense radiation , particularly DNA-damaging radiation. Since the vacuole of a plant occupies most of a mature cell, this helps protect the DNA in other organelles.