Best avenue to get prestige level 1 for the relic appearance as a casual, PVE prot pally

Hey all, so basically what title says.

I LOVE the PVP artifact appearance for prot paladins and would love to have it, but I am fairly terribad at PVP and tend to concentrate on PVE content. Should I just queue into random BGS and hope for the best?

Also roughly how long could I expect to be working at it?

Thanks