Is there a lower limit to the age at which one could first determine that a child is homosexual?
If so, what age is it?
EDIT: TL;DR -->I do not believe there is an age cap. From the moment the child is born, they learn from their surroundings and parents how to act/react to all situations. Some parts of a child are nurture (how they handle anger, gender roles, etc...), some are nature (liking sports vs art, etc...), but children are just experiencing life, they do not categorize themselves like we do.
I inferred some things about the OP's question because as it stands explicitly, the answer is a very short, "No". However, I felt that was unhelpful answer so I inferred that the OP must have had more going on behind the scenes that wasn't expressed in the post.
Children learn about life by watching others and by guidance from their parents. My 5 yr old boy likes to paint his nails because he has watched my wife do it. By no means does that mean he is homosexual. He simply saw someone else doing it, and tried doing it himself.
What ever the child you are thinking about is doing, he/she is probably just getting influence from other sources like TV or school. It is up to you to guide your child as you wish. If you want them to be homosexual, by all means tell them their behavior means they are homosexual. If you do not want your child to be homosexual, realize they are just experimenting. Possibly tell them that is something the other gender usually does, but do not prohibit them from doing it because the child really is just finding out about life.
Another example is when my 5yr old was putting my wife's hair ties and such in his hair, or putting on her bra. I just told him he was "being silly, putting on mama's clothes" and such. And he really was, he just likes being silly. He grew out of that and now likes to be silly by dancing all crazy like.
EDIT: nocomprende wrote a comment that I feel should not be missed, so I got his permission to put it in this answer.
"...we [adults] have a definition of homosexuality, but children simply have preferences and behavior. We think that a definition makes something so, but there is no homosexuality until there is intent. That is in the mind, not visible. It makes no difference until intent is acted on."
As NoComprende says, we should see that our children ARE innocence. They ARE kindness and love. That is what they are made of at a young age.
As a personal rant, unfortunately in our society, "growing up" could be defined as the process of losing that innocence, love, and kindness.
I have some experience with this as a parent! So speaking from experience: there is no set age at which you can tell what a child's sexual preferences, gender identity, gender expression, political tastes, favourite baseball team, or preference for cats versus dogs are/will be, but there is one critical thing you can do to make that age earlier than it otherwise would have been. Some of those things in the list are facetious, some of them are likely nature, some are nurture, and others are choices, but all of them are affected the same way by doing this one thing:
Make sure your child feels confident and safe telling you about their life, thoughts, and feelings.
Feeling safe and confident comes from knowing that they are loved and that they don't risk personal rejection for revealing something. How you react any time they reveal something they feel sensitive about is a test for the next time they have something on their minds; each time you react positively and without judgement gives them more confidence that you won't reject them, and makes it more likely you will be shared with in the future.
So though there is no age limit, you can help ensure your child will reveal personal things earlier rather than later (perhaps much later), by ensuring they feel that they will always be accepted by and acceptable to you when they do.