Hi @Worldwideweb , welcome to Trusted House Sitters 
Getting your first sit is always the tricky one and how long it takes depends on quite a few factors.
How many applications are you sending out and how flexible is your destination choice will both make a difference
When we started it took us a couple of weeks to get our first sit - however, we were applying to many sits and received over 20 rejections before getting accepted.
Getting your first sit has been discussed many times on the forum, have a look at this thread for some great advice from experienced sitters