Streaks of sunlight make way through the holes in the roof.
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If I "make way" for someone else, I am getting out of his/her way so that he/she can pass.
If I "make my way" in a direction, I am traveling in that direction.
In your example, the sunlight is traveling, not standing aside so that someone else can pass through the hole in the roof. (Although that would be entertaining to see!) So your example is incorrect. Don't be concerned that the sunlight is not a person or other animate actor. From a grammatical perspective, it can still have an appropriate pronoun between make and way:
Streaks of sunlight make their way through the holes in the roof.
Note the use of the plural form their, because the subject is the plural noun Streaks. (The prepositional phrase of sunlight modifies the noun Streaks.)