All three men were already at or near the top of the political ladder when the triumvirate was formed.

Crassus had already served as consul. Crassus had some military success in the Civil War and in the Third Servile war, and of course was proverbially the richest man in Rome. He had served in pretty much the whole of the cursus honorum. That kind of wealth and political power meant he was perhaps the single most powerful man in Rome.

Pompey at the time was the greatest general of the day. He had celebrated multiple triumphs for his victories. He had also served as consul, but it seems he may not have followed the traditional cursus honorum. He seemed to have skipped several of the steps, and a couple of his triumphs were held when he was too young to properly receive one. That was Pompey in a nutshell, he was always ahead of his peers. After his campaigns in the East he rivaled, and perhaps exceeded, Crassus for wealth.

So the two of them were already perhaps Rome's most influential men when the Triumvirate formed. They had held the top political job. They were both successful generals. They both were fabulously wealthy, and had large networks of patronage. Although they disliked each other. They were basically each other's primary nemesis. Julius Caesar by comparison was younger and less experienced than either of the other two. But even he was by that time a major political player. He was the Pontifex Maximus (the senior leader of the Roman religion), and he had just returned from Spain where he had served as propraetor (governor). He had also by then become wealthy... although nowhere near as wealthy as the other two.

The Triumvirate was then an alliance between the two most powerful men in Rome, and a man who seemed likely to join them at the top pretty soon. The conceit was that together they would be irresistible. The fact is they weren't ever as dominant as all of that. Other senators could and did resist the trio. But when and where they really wanted something they nearly always got their way.