Evolution is not continuous, because it is based on discontinuous data. In other words, even if evolution was continuous (for the sake of argument) discontinuous fossil data would make it impossible to prove that, since discontinuous data better support a discontinuous model.
Let me create an analogy. I make a continuous circle of popcorn, so each piece of popcorn touches the next. This is analogous to the circle of life where all the data is accounted for.
I go to get the experts to see the circle. But as time goes by, birds eat the popcorn and what remains of my continuous circle of life, is no longer continuous (random fossils). It may still appear to be expressing a circle, but it is now a broken circle with gaps. Even though it was originally continuous, based on the remaining popcorn data, you would need to infer discontinuous. I could not prove the circle was continuous even if I made it. The experts would deny this was true based on the broke circle they see.
The scientific method will not allow you to infer what the data does not say. In the case of the popcorn circle, although the circle was continuous initially, the broken data will not support this truth. There is a break down in the method.
A better way would be to start with an aspect of data (modern things) where we have all the variety in place instead of bits and pieces. For example, we have that with humans and will see what appears to be a continuous progression. People often don't think modern human evolve because they expect to see fossil jumps and not continuous change that is less obvious.
We don't need tonsils, but humans retain these. They go away slowly into the setting sun and not disappear like a discontinuous model might imply. If only have a hundred fossils spread over 100K years, we can create a discontinuous impression.