Intellectually, no. The intellect forms concepts of observed phenomenon, so conceiving something infinite with finite tools, doesn't work.
However, there is a way... and perhaps a few people have glimpsed this, and so have a conception of infinity, but it is an experience rather than a thought-concept.
The general notion is that we are beings of consciousness, but we are entirely convinced that our consciousness originates in the head, behind the eyes somewhere. This is a fundamental fallacy, and drives our current highly materialistic analysis of existence.
Under extremely close observation, through meditation, experience shows that consciousness actually originates from the heart, in its fullness. In a sense, consciousness 'in the head' is a dimmed reflection and version of the real thing, which is also why the intellect is a reflective tool, and not the real thing. It can only approximate things (and get very clever with it, such as developing calculus!)
The consciousness that pervades creation is in essence the very same consciousness that animates all beings, rather like the hub of a wheel, with all the spokes radiating outward.
Hence, residing inside that consciousness, is also an experience of infinite radius. There are texts in traditions such as Zazen (i.e. zen) that treat clearly the different steps, and how various aspects of ego drop off in the process. It's a well trodden path.
So from that perspective, it's possible to really conceive what infinity means, even if the 'usual' mind doesn't get it.
Wow, did I get esoteric there!