Hi OP. I'm a man (in my 30s) and wondered if you would appreciate some male advice. Firstly, I think you need to believe in yourself. There will be a man out there who will want to choose you. You've got friends, a job. You work in early years, so you are probably not motivated by money, empathetic and caring. These are all good, attractive qualities. I'm sure your friends could point to many more good things about you - ask them! Many people are not good at small talk and are clumsy (I know I am) - it doesn't prevent relationships. Being confident in and about yourself is a very attractive quality.
You said something interesting in your post, which was that you just assumed it would happen. My single female friends in their 30s have all been waiting for a man to come along, spot them and ask them out. But that doesn't necessarily happen - most men I know are really quite shy and afraid of making the first move without some signal the woman is interested in them. Most of the couples I know knew each other in real life, as friends of acquaintances, before getting together.
If OLD isn't right for you, you obviously need to put yourself in situations where you will meet compatible, single men. That means e.g. sports clubs, walking groups, book clubs etc (whatever is your interest). These would also be a good way of getting your confidence up about speaking to men, in a neutral, non-dating setting. Yoga may be too female dominated a pursuit for this purpose.
If you work in Early Years, could you talk to the Dads of children - not as a way of finding a date, but just as a way of getting confidence about talking to men before dating? Tell them something interesting about what their children did; ask about their day etc.
When you are in a setting where you have single men you might be interested in, you need to subtly let them know you are available. So e.g. make a comment that shows you are single without being too obvious about it. Otherwise men will assume you are attached and not want to bother you. Be interested in what they say (assuming it is interesting!) and engage them in conversation about your mutual activity etc. Again, if you are too shy, men will assume you're just not into them (though coy shyness can be attractive).
I hope this helps, and good luck. You will find someone!