1. Suprise. Struck hard and fast before the inner sphere even knew of their existance.
2. suposedly superior troops. Bred to wage war, with superior genes.
3. Far more advanced technology. Everything that the clans had was superior to the inner sphere version, and had technologies lost to them.
So how exactly did they survive that first war?
The clans culture is what lead to them losing. When the attack a world they use a bidding system to deploy the least amount of resources to take the planet as possible. This process forced them to fight hard and well because they couldnt just mass swarm their enemies. Where this started to back fire is when the Inner sphere used it to their advantage. House Kurita and the Federated Commonwealth developed a good understanding of clan tatics and took some of their elite units and forged new units with fresh histories. So during the bidding to see what forces the clans would deploy they went into the battle expecting to face Green troops and they actually were fighting the Inner sphere elite.
Further more there was a divide in the clans. 2 factions called the Wardens and the Crusaders. The wardens didnt want to fight the inner sphere but the crusaders wanted to conquer them. A political infight lead to some major stalls in the clan push, allowing the Inner sphere to prepare. Ultimately what held the clans back was when Comstar intervened and pulled out a massive army of Lostech machinery they hard secretly stored. The fight was negotiated using the clan bidding system and the penalty for the clans failure was to not advance into Innersphere space for 10 years. Some elements of the clans force had an ego complex and pushed in too far too fast and were utterly destroyed. Of all the clans only Wolf actually succeeded in its objectives.
The clans were excellent 1v1. However group warfare was more balanced. Alot of the Clans failure was believing that freeborn mechwarriors were inferior.