@fast,
But I think the arguments as to whether electrons exist, in particular, is quite a different class of argument to the philosophical argument as to whether 'we experience anything directly' and should not be subjected to the same critique.
There are specific problems suggested by quantum physics, notobaly, the 'double-slit' experiments which demonstrate that electrons exhibit both particle and wave characteristics, which defies any common sense notion of physical ontology.
Then there are the associated problems created by Bell's experiments showing the non-locality of quantum relations, of the type that caused Einstein to exclaim that he refused to accept spooky-action-at-a-distance.
In both these cases, the model of quantum mechanics seems to contradict the idea that electrons and photons can be thought of as 'points' or 'particles'.
Hence the question in the OP - to what extent can electrons be said to
exist?
The question can be taken also as question about the definition of the word 'exist' in relation to sub-atomic particles.
And as much of materialist ontology is posited, consciously or othewise, on some species of atomism, or ultimately existing point-particles, this raises a general question about ontology.