@limehat31,
In my opinion, the preferable verb form is "encourage."
"We want to provide the quality of goods and services that ENCOURAGE employee confidence."
1. We want to provide the quality of something.
2. What does "something" refer to?
3. I feel that it refers to "Goods and services that ENCOURAGE employee confidence."
Compare:
"The quality of goods and services that ENCOURAGE employee confidence is what we want to provide."
I feel that the relative pronoun "that" clearly refers to "goods and services."