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Certainly! Sweet peas (Lathyrus) can be successfully transplanted from seedlings. Start the seeds indoors and allow the seedlings to develop a few sets of leaves. Transplant them into a well-prepared garden bed or container with rich, well-draining soil after the last frost. Gently remove the seedlings from their pots, place them in prepared holes at the appropriate spacing, and water thoroughly. Sweet peas prefer cooler temperatures, so transplanting should occur after the soil has warmed up. Provide support structures for them to climb as they grow.

Since they are very cramped in that space, I would recommend trimming off the stem of some of the unwanted seedlings to kill them, rather than trying to untangle root masses. Try and refrain from disturbing the root structure, since these can be a little more sensitive to this practice.

https://www.gardeningknowhow.com/ornamental/flowers/sweet-pea/care-of-sweet-peas.htm