I think you're putting way too much pressure on this guy being 'the one' because, understandably, you want to find the right person, settle down and not be hurt anymore.
But that's only gonna put you at more risk, putting all your eggs in one basket so to speak. Statistically, the vast majority of relationships fail. You've only known this guy a few months and it's been a few days since you started something romantic. At this stage it could go either way. But if you let yourself get carried away, it's gonna hurt a lot more if it turns out he's not interested, you're not compatible or whatever.
It's crucial not to tie your self esteem up on whether or not he likes or wants to be with you. Even if it doesn't work out you're still a person worthy of love and care and respect.
I understand the fear at the beginning of something new, I'm the same after having my heart broken a few times and dealing with a lot of loss in my life. It takes months for me to start truly enjoying it and relaxing instead of constantly worrying and monitoring for it going wrong. All you can do is remind yourself to chill out, not expect anything so soon, and remember this stage is for you to assess if he's right for you as well as the other way around!
Keep your feet on the ground, don't give more than you're getting. Take it as 'if I have some fun times with this guy that's great, anything else is a bonus' as if you're going into this with 'omg is this gonna work out, is he the one? Will he hurt me! Does he like me? I can't stop thinking about him!' He'll smell it a mile off and run the other way, it's deeply unattractive and sorry to be harsh, but tends to suggest the other person isn't quite in the right place to date or emotionally stable/sorted enough.
People want to date people who are self assured and confident and not desperate. Most people like a challenge. I don't mean playing games, but don't be at his beck and call from day one, the early stages of dating should be both of you sussing each other out cautiously while getting to know one another.
I feel like you're asking how to let your guard down but it's up for a reason. It's there to protect you. It's sensible. If six months in when you're exclusively dating and in a serious relationship you still feel this way then that's a problem. But right now you barely know him and he barely knows you. You're right to be cautious! Don't go trying to force your guard down for someone who hasn't earned it yet.