Yes, you can play singles in padel, but it’s much less common. Padel is designed as a doubles game, and the court size, angles, and pace all suit four players. There are specific singles courts (which are narrower), but most clubs — including ours — use standard doubles courts.
If you’re just two people and want to hit, go for it and try cross court - hitting diagonally to each other! It’s great for practice, but the real magic of padel is in the doubles dynamic.