It can be done. The personal references don’t “count” as much with hosts as reviews from members, so it will be helpful to get a few of them from friends and relatives you’ve sat for. Photos of you loving dogs and/or other pets you might be sitting will be helpful. Emphasize your petowning experience including any experience you have giving medications, etc.
The more desirable the location the more competition there will be, so you might consider doing a few more local easier to get sits to build up site credibility and get some reviews.
I’ve already been warned to stay away from even mentioning current world conditions that might impact on homeowner decisions regarding picking sitters from some countries. So I will only say that homeowners want people they are comfortable with and whose values align with theirs so don’t be afraid to mention some related stuff in your applications.
Also please be aware that petsitting is considered “work” in many countries, so best not to mention that if you are travelling as a tourist. There’s a forum thread here that you might want to checkout: https://forum.trustedhousesitters.com/t/challenges-with-border-guards-re-the-laws/