The modal cosmological argument (MCA) has numerous variations. Here's one I'm currently working on, which makes use of a weakened Principle of Sufficient Reason (W-PSR). First, it's important to understand some key terms:
contingent: x is contingent if and only if x possibly exists and x possibly does not-exist.
Examples: trees, mountains, animals
necessary: y is necessary if and only if y exists and cannot not-exist.
Examples: God, abstract objects
universe: sum total of all physical space, time, matter and energy.
1. Possibly, everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. (Premise, W-PSR)
2. Possibly, the universe as a whole does not exist. (Premise)
3. Hence, the universe is contingent. (Implied by 1 and 2)
4. Possibly, the universe has an external cause. (From 1 and 3)
5. Necessarily, if the universe has an external cause, that cause is a timeless, changeless, immaterial and very powerful entity, e.g. God. (Premise)
6. Possibly, God exists. (From 4 and 5)
7. Hence, God possibly has an explanation. (From 1 and 6)
8. Necessarily, something timeless and changeless cannot have an external cause. (Premise)
9. Hence, God is explained by a necessity of his own nature. (From 1, 7 and 8)
10. Therefore, God exists. (Implied by 9)