Glulam is probably three times as expensive as construction timber, calculated per volume unit. With a 7-meter span and center-to-center distance of 600 mm, the beams would need to be approximately 70x360 mm in cross-section, so it's not an option. With a glulam beam in the middle, resting partly on the garage wall and partly on a post in the middle of the carport entrance, you could solve it quite easily. To provide a hint about suitable dimensions, information about the depth of the carport is also needed.