My puppy is too submissive?

I was just wondering if its normal for my puppy to be as submissive as he is or if I should be worried and do something about it.

My puppy is a 4 and a half month old pure bred border collie very active adorable and intelligent little thing. I went to see his litter before picking a puppy at 8 almost 9 weeks old and I chose him because I felt bad for him since all the other pups were barking and playing and he was trying to just squeeze himself in the smallest little corners. When his siblings play fought him hed lay there and wait for them to finish biting him or hell squirm out and he wouldnt fight back I felt bad since his siblings were hurting him hed cry when bitten. His siblings played and barked trying to get our attention and where was my puppy? Oh he was squeezing himself between the wall and the bookcase far from us… He continued the squeezing into tight places phase until he realized he was too big and was getting hurt when he tried
Hes 4 and a half now fully vaccinated and went through an obedience class the trainer in the class adored how he was amazingly social. Her and I have different ideas apparently on what being social means. Every class this was for 4 months old puppies and younger he would get attacked by either a Chihuahua or a.. what looked like a wiener dog in a Chihuahua size. Somehow my puppy that is 5 times their size ends up on his back getting bitten by them on his neck crying for his life every class she had to separate them. My puppy was the only one that ever got attacked in that class.
Now we try to take him to dog parks he loves seeing other dogs gets so happy and excited like crazy he ditches us starts wagging his tail runs towards these dogs and a foot before he reaches them hed lay down as close to the ground as possible. He hides his butt when some other dog tries to sniff it but hes okay with sniffing other dogs bums. He lays flat and ends up being surrounded by other dogs trying to sniff him he lays then on his side or back. I try to have the dogs back up every once in a while to see if hes doing alright and what hes doing is by choice. Apparently it is?
He has gotten nipped by a dog at least once everytime we go to the park. Most times he doesnt cry though. Other dogs walk all over him when we play fetch and they run after the ball he stops or backs off and just watches them as they take his ball and stays in place.
Even when he meets a dog and he lays flat and the dog accepts him and tries to play with him he seems.. to neglect it I guess. Like this one time He laid flat before meeting a dog and the dog was adorable and liked him and started rolling over doing tricks wagging his tail and all my dog was doing? He was trying to not make eye contact with him and stay on the ground the other dog nudged him with his snout to get him to roll over like him he even tried rolling over on him but my puppy looked like a selfconscious no selfesteem geeky nerd getting beat up who was taught not to fight back where he was aware of what the other dog was doing but pretending not to be purposely not making eye contact Im not sure how to explain it
Ive had him go on many many one on one play dates with puppies his size and age and some of them tried to show submissive behavior but then hed work harder to be even MORE submissive then them. But most of the time the same thing happens all over again.

I dont know what to do?
Im thinking of not taking him to dog parks till hes an adult which will be difficult to find a good substitute I just dont know whats going on? Hes AMAZING with people the vet loves him and says hes happy and healthy the trainer thought so too but none of them have seen these behaviors. Will he just grow out of it? Recommendations?

I plan on signing him up for another obedience class but it would be nice if he could play with dogs without being too occupied making them know hes submissive

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