The only thing I could think of that comes close to explaining the trinity without conceding that it's not supposed to make sense is if you imagine God to be like a three-headed hydra with each head corresponding to the Father, Son, and Holy Spirit.

1. It is monotheistic: In most religious traditions, if you have a god with multiple heads, you would just say that the god has multiple heads. You wouldn't say that multiple gods share the same body. Thus, this hydra conception preserves monotheism.

2. It isn't God wearing three different masks: I forgot the name of the heresy, but the heretical belief is that the trinity is just God wearing three different masks like ancient Greek theater. The three-headed hydra isn't heretical in that sense because the three heads have distinct personalities. When Jesus laments of being forsaken by God the Father, it isn't God talking to himself, but a hydra head pleading to another hydra head.

3. It presumes each part of the trinity is eternal: There's various related heresies that try to subordinate one part of the trinity to another, usually the Son being subordinated to the Father for obvious reasons. So one heresy is that Jesus started out as human but became God. Arianism also has this subordination as well. The three-headed hydra conception doesn't have a hierarchy. All hydra heads are equal with respect to one another.

Apparently, there is art that depicts the Trinity as a dude with three heads, but I guess this isn't popular because it's resembles Hindu religious iconography.