Answer:
there is not a flat answer to this. First i would not cook beef burger while frozen in oven. I would defrost it first. Also depends on how much of it you have - by weigh and thickness, to say how long.
Beef should be cooked until it is no longer pink in center.
Ill say its a 1/4 # burger unthawed, baked at 350 degrees . it would take about 15- 20 minutes. Id say , but dont do it by time. Do it it by how it looks . when cooked ,It should be firm, but not hard, and not pink in center. Use a cooking thermometer. Cook beef to 165 degrees at thickest part.