I don't think framing it as 'the one' is really helpful, as there will be potentially hundreds of 'the one's when it comes to a therapist. There isn't just one therapist out there that's perfect for you that you have to find. There will be many who are good enough to meet your needs. The pursuit of perfection in therapy is tricky because it can lead you to discount perfectly healthy and helpful relationships over a small conflict or disagreement, when in reality research shows that the therapeutic relationship is stronger after rupture and repair than before any rupture at all!
Generally though, it's in two parts. Credentials, and personability.
Do they have the correct credentials for your goals? What are you aiming for? If you're looking to process a bereavement then a person-centred counsellor trained in bereavement would be the one to look for. If you're after treating OCD, they won't be right for you and you need a CBT therapist. Going to someone for a problem they're not properly trained in working with can be futile at best, harmful at worst. Always make sure they are professionally registered and accredited as there are lots of people out there claiming to be therapists with no training. Check the professional register.
Personability: do you feel comfortable with them? Do you feel as though you could tell them anything and they would respond appropriately? If you question or challenge something they say (for example 'it sounds like you feel angry' 'no, not anger, disappointment') do they go with the flow and accept that or do they get defensive? Do you get the impression they care and are genuinely listening and feel positively about you, or are they disapproving and very clearly clock watching? Can you sense that they're fully 'with' you in the moment? Some people want a therapist who's a complete blank slate who'll say very little other than reflecting. Others find that infuriating and need back and forth!
I think one session is absolutely enough to discount a therapist, but it may not be enough to be certain that they're right for you. You can stop seeing a therapist at any time for any reason, so you can always stop and find someone else if you feel it isn't working. Sometimes relationships do grow, the first meeting can often be a bit awkward on both sides as it's such an artificial situation when you think about it, you're meeting a complete stranger for the very first time and expected to share your deepest emotions and thoughts, one sided, while knowing nothing about them. You're aware you're both only there because one is paying the other (if private). It can take time for it to feel relaxed and normal but you should feel empowered to trust your gut.