What does the bold-faced part mean?

What does the bold-faced part mean?

The passage below is from Fathoms: The World in the Whale Hardcover by Rebecca Giggs.

‘Historic time overlaps with geologic time the way a whale-louse overlaps with the blue whale it infests’ —this is by the American biographer and nature writer Verlyn Klinkenborg in Yale’s E360 magazine. Klinkenborg goes on, ‘the scale of that comparison is too small by several orders of magnitude, yet it’s all too easy to believe, with the self-importance of a whale louse, that we exist apart’. If lice are indeed egotists, we inhabit time as they do: with mystical regard for the materiality of the deep time we imagine is beyond our influence. The whale’s moment, meanwhile, is inestimably, insensately long.

In this passage the author tells readers the infinitesimalness of historic time to geologic time and warns the hubris of human forgetting this like whale-lice.

The bold-faced part seems to explain the reason of human forgetting, human arrogance. (Am I right?)

But still I am in the dark.

First and foremost, I cannot figure out the subject of ‘is beyond our influence’.

Not knowing the subject the whole idea of the part isn’t put together.

Second, ‘with mystical regard’

Regard in this context means view. (I’m sure about this.)

But mystical is so mysterious. Dictionary shows a number of synonyms like arcane, cryptic, enigmatic, mysterious, mystic, etc. But it doesn’t help. It seems to be able to have both negative and positive nuances. But I decide it is used in negative sense here. (Am I right?)

Last, ‘materiality of the deep time’

Here ‘materiality’ seems to mean concreteness, not intangible. (Am I right?)

Thanks in advance.