It depends on what exactly you mean by “plant” and “animal.” There are much more fundamental divisions between life forms than that between multicellular plants and animals, and the former “Kingdom” system is no longer adequate for classification.
There is a much more fundamental distinction between what are called “procaryotes,” including bacteria-like forms, which have a very simple cell form, and “eucaryotes,” including protozoa, algae, other unicellular forms, plus multicellular plants and animals, which have much more complex cells.
But it has been found that there is an even more fundamental genetic distinction within procaryotes, between a group called “Archaea” and other bacteria. Because of this, modern classifications recoginize three “Domains,” a level higher than Kingdom, Archaea, Bacteria, and Eucaryota.
Within bacteria, there are photosynthetic forms, the cyanobacteria, formerly called “blue-green algae.” In some sense these are “plants,” in that they manufacture their own food from sunlight, but they are not closely related to multicellular plants or other kinds of algae.
Even within the Eucaryota, the “kingdom” system doesn’t work very well. It has been a practice over the past few decades to recognize four kingdoms within the Eucaryota, the Protista for one-celled forms, plus the multicellular Plantae, Animalia, and Fungi (which are neither plants nor animals). However, the Protista themselves are quite diverse, and include some forms which are more closely related to plants, some to animals, and some to fungi. A real classification would probably have to recognize probably twenty different “kingdom-level” groups within the Eucaryota alone.
There were probably types of archaea and bacteria, including cyanobacteria, that were capable of living on land at very early periods. Likewise, simple algae may have colonized the land early in their history. The earliest fossils of multicellular land plants are from Silurian, 425 million years ago. It is possible that multicellular animals may have colonized even earlier than this, to feed on terrestrial algae or fungi.