Sala'am Doaa
The form 'overcoming ' is correct, and the reason for this has nothing to do with the word 'to'.
If you think about the phrase 'the key to the door' , the phrase 'key to' is followed by a noun phrase: 'the door'. And even when you are using the word 'key' in a figurative sense, the word 'to' still needs to be followed by a noun phrase.
In your sentence above you have a long noun phrase, starting with a verb. And how do you make a verb do the job of a noun? You add 'ing'. This form is called a gerund, and verbs usually take this form when they are the subject or object of a sentence. 'overcoming' is does the job of a noun in this phrase, in the same way as 'door' is a noun in the example above.
I hope that's clear.