If the Ancient One had been alive when Thanos started his quest to obtain the Infinity Stones, she could’ve dealt with him in a number of ways
Thanos didn’t personally involve himself in the fight against Earth’s heroes until great and powerful beings like Odin and the Ancient One were already dead.
The Ancient One was the Sorcerer Supreme and had lived for at least 700 years, kept alive by tapping into and drawing power from the Dark Dimension. As the Sorcerer Supreme, the Ancient One had complete Mastery of the Mystic Arts and could’ve used a myriad of spells and tactics to defeat Thanos before he obtained the Infinity Stones.
As the Sorcerer Supreme, her mastery over the Mirror Dimension, astral projection, and time manipulation gave her abilities that a base-level Thanos or even one with a few stones would have struggled to counter.
We witnessed how dangerous the Mirror Dimension was and how it was possible to get trapped inside. A powerful Sorcerer like Strange or the Ancient One could transport themselves and others into the Mirror Dimension but the use of a sling ring was required to be able to leave.
The Ancient One had spent hundreds of years honing her craft and could’ve transported Thanos into the Mirror Dimension and left him there to die. Thanos did not possess a sling ring and would have no means of escape.
And those who used the power of the Dark Dimension, like the Ancient One, had a stronger control over space and matter, in the Mirror Dimension, than they usually would, to the point of being able to fold and warp space in reality. In such a pocket dimension where physical strength is useless and reality is controlled entirely by the sorcerer, Thanos would have no chance of defeating her.
The only being who escaped the Mirror Dimension without a sling ring was the Scarlet Witch by using her chaos magic to warp reality. Thanos did not possess this power and would’ve been trapped in the Mirror Dimension until he died.
Another way the Ancient One could’ve defeated Thanos was by replicating one of her most impressive feats when she knocked Bruce Banner's soul out of his body. The Ancient One could land a single strike and separate Thanos from his physical form, leaving him incapacitated. Thanos would have no defense against that.
The Ancient One used the power of the Time Stone (housed inside the Eye of Agamotto) during her centuries as the Sorcerer Supreme to study alternate futures and protect Earth, and it’s not unthinkable that she used its active time-manipulation powers to deal with serious threats.
She simply could have frozen Thanos in place, moved his body and opened up a portal slicing his head off, sending it God knows where. Her experience and mastery over the Time would’ve given her countless opportunities to defeat and kill Thanos.
The Ancient One had the power to manipulate energy, create tangible shields, and summon dangerous pocket dimensions. With the Time Stone, she had the ability to control time and to some extent shape reality.
As the Socerer Supreme, and consdering her immense power and knowledge in many aspects of Magic, there were many ways the Ancient One could’ve have put an end to Thanos long before Infinity War.