against (all|the|all the) odds

used to describe a situation where something or someone succeeds despite facing very difficult or unlikely circumstances

Against all odds, he managed to complete the marathon despite suffering from an injury.
Against the odds, the underdog team won the championship, surprising everyone.
Against all the odds, he recovered from a serious illness and resumed his normal life.
Against all odds, the small business thrived in a competitive market.
Against the odds, she achieved her dream of becoming a successful entrepreneur.