The problem of induction. We must assume a past and a future, but these concepts cannot be verified using the empirical method. The Atheist world view just has to "assume" a past and future exists, which is being arbitrary and ad hoc. It's an assumption that isn't backed up by any form of empirical reason.
The status of immaterial objects. If a past and a future do exist, where are they located in the material universe? They need to exist in a mind, yet they would be true even if no human minds existed to conceive of them.
No properly basic beliefs. Empiricism does not allow for circular argumentation. Yet properly basic beliefs (such as numbers and words) cannot be proven without engaging in circularity I.E numbers prove the existence of numbers, words prove the existence of words. There is no possible way to prove numbers without invoking numbers and words without invoking words, demonstrating that empiricism is lacking here.
The problem of the external world. How can we know that our perceptions accurately represent reality? If our access to the external world can only be via sensory experiences (which can be subject to error), how can sense data alone be the basis for knowledge about the external world?
These are 4 off the top of my head, but in my mind they are critically damning of philosophies providing a framework for an Atheistic worldview.
I would say that these are not particularly good reasons for rejecting even materialism or empiricism, let alone other possible atheist perspectives:
The problem of the external world - All knowledge is subject to error or uncertainty, so what? That's a brute fact
whatever worldview one adopts, but the fact remains that empirical information has so far proven to be by far the
most reliable way of knowing about reality we have.
No properly basic beliefs - I'm not sure this one even makes sense; observing the utility of words and numbers demonstrates the utility of words and numbers. How is that circular?
The status of immaterial objects - This seems to depend on the assumption of a strictly linear, non-relativistic view of time. If instead we live in a four-dimensional spacetime and our passage through time is not fundamentally different from our passage through space, it would be perfectly coherent to suppose that all past and future moments do materially exist. Ironically many if not most theists hold quite a similar view in terms of their gods' omniscience; the view that God is 'outside time' would require that our passage through time is passage into something that exists and is already observed. For this to be a valid criticism, you'd first have to prove that a linear, non-relativistic view of time is correct or at least probable.
The problem of induction - Past and future cannot be directly observed (regardless of the nature of time), but at most that's only a problem for the narrowest caricatures of empiricism. Empiricism might be roughly described as the view under which things are accepted only on the basis of convergent observations by oneself, or other reliable observers, or things which are necessary to explain such observations. For example it's likely that virtually all empiricists accept the existence of neutrinos, even though they can't be directly observed, because they have observable effects on experimental wossnames which otherwise cannot be easily explained. Similarly, the reality of the past, of previous futures and of the remaining future are necessary to explain direct observations of reality now and in the future.
To be fair to your point on induction, when they think it's situationally convenient to do so many debating atheists
do readily indulge in the narrow caricature of empiricism against which it would be effective: Some common theist arguments such as cosmological and fine-tuning posit that a deity
is necessary (or at least most plausible) to explain our observations about reality, and in order to both uphold the "no evidence for theism" doctrine and also avoid the hard intellectual work/onus of explaining our observations by other means, it's obviously quite common to see atheists insisting on an empiricism which rejects inference, on those occasions. In fact they often go even further (again, when situationally convenient) and reject even that middle clause of 'other reliable observers'; called "testimonial
evid claims" or "hearsay," when they choose to take that approach.
But I don't think that undermining the inconsistencies, arbitrary rhetoric and special pleading of one of the lower tiers of atheist thinkers (I've taken to thinking of this as the NONENB, no onus/no evidence/no belief trend of mostly-internet atheism) really constitutes a viable reason for rejecting atheism in general.
Space and time aren't particularly abstract (let alone transcendental) concepts at their core, they're direct and inescapable inferences from our constant daily experience. It can obviously be tricky trying to really wrap our minds around them, like trying to describe the box we're inside, but the bare fact that the box is there isn't obscure or confusing. The modern discovery of relativity is confusing, but from what I gather it pretty conclusively demonstrates that spacetime actually is a real 'thing,' not just an inert backdrop but something which actually interacts with mass and energy.
