you better try to get some reviews or sales from different locations and countries ( from your friends or connections ), that will add more benefit than those backlinks
And what kind of service you are providing in Fiverr?
Backlinks Service
And you are asking how to rank your service at Google? Anyways no idea if it works but as other said, try to get reviews and few sell at first. Fiverr algorithm is hard to cope up with. There is a guide at BHW how to start the business at Fiverr, and the guide was excellent. I can't recall now. If I find I will post it here.