Ive always thought  that for such an iconic character.. Caps background story always seemed to lack. Well backbground.  
Despite his bravery &somewhat outdated (even for 1940s America) sense of nobility, his characterisation before the serum has always been somewhat ill-defined.its almost as if theres this missing "spark".  
Bruce Wayne has the ultimate tragedy, Kal El the ultimate gift/purpose.. Parker has..well u get the idea  
This ladies &gentlemen is MY take on the Captain America background origin treatment.

Steve Rogers was born to an Irish immigrant  father (Celtic ancestry) &Native American mother (herself a Pontiac named Running Star by her father Standing Eagle) shunned ffrom the "settlements" for falling in love with a white man &equally shunned in the Red Hook/Brooklyn where they eventually settled for being "Injun"  they struggled to make a life together for them &their soon to be born child. 
Though mostly adopting his fathers features (apart from the uncannily olive complexion)  he would also be shunned by  most of the neighbourhood kids for his mixed lineage/Native mother &his sickly scrawny appearance, all except of course for one James Barnes who lived 5doors down &helped him fight off the neighbourhood gullies &street gangs..  
 
The man Steve Rogers would call father was a celtic prizefighter from a long line of fighters known for their skill &grit who came to America searching for a better life, he would teach his son the art of boxing passed down to him by his father before him as soon as the child was able to walk, much to the chagrin of his more gentle natured mother 
He kept doing this despite eventually realising his son would NEVER live up to the physical prowess he or his his legendary GrandFather (Jack Rogers) possesed, he also continued to train/spar with his son for two reasons 1 he knew his son had immense heart..which to him was just as important as strength &2 possibly as a way of bonding with him because as he grew older   he realised he&his son had very little in common,  
little Steve excelled in History, Math (esp trigonometry) &Art he preferred to spend his spare time drawing &reading endless piles of history books on all the great philosophers &military tacticians of centuries past  ie Aristotle, Alexander of Macedonia etc &was fascinated with stories of bravery &sacrifice of  Spartan/Roman generals & tomes of the iilyad  etc(sic) he would take his appreciation of Spartan military to rificulous lenths practicing with a garbage bin lid..which got him ridiculed by passers by &picked on &savagely beaten by another, despite his attackers size &strength however he remembered how the soldiers he idolised stood up to an army 1million strong &thought if they could so can he.. It didnt work.. Gus Kowalski wasnt a million Persians &he was DEFINATELY not 300 Spartan warriors..despite this he did not run &was almost hospitalised as a result... The incident had a profound effect on him.. One that would stay with him to this very day 
 
After the garbage lid incident followed tryouts for football & the QB position (no doubt in order to please his ailing father) were initially laughed off, but while suprisingly &unexpectedly successful also woefully shortlived..  At first only allowed to scrimmage as a joke  
his unnearthly vision, accuracy, quick thinking, technique &bravery were quite prodigious... &shocked many onlookers. 
These qualities however were NOT complimented by much needed physicall prowess or stamina.. his weakness &frailty eventually proved costly &after an untimely &spiteful tackle outside the pocket put him in hospital for 4weeks.. But earned him the respect of the entire school for even trying &doing aswell as he did 
While recovering &taking a break from being bullied by the street gangs he'd improve upon his art &dream about being "more useful" his parents who had taken ill shortly before he was hospitalised made a turn for the worse &died of influenza while he was recovering.
He is allocated to a salvatian army boys home before he even fully recovered.. On his last day in he is told the news.. On his first day out... 
 
He see's the recruitment poster.....  The rest as they say is History.