"just at the time that I dated my creation" in Frankenstein

In the last paragraph of chapter 3 (of the 1823 edition), when Frankenstein was on the verge of completing his work, he was “oppressed with a slow fever” making him “nervous to a most painful degree”:

The leaves of that year had withered before my work drew near to a close, and now every day showed me more plainly how well I had succeeded. But my enthusiasm was checked by my anxiety, and I appeared rather like one doomed by slavery to toil in the mines, or any other unwholesome trade than an artist occupied by his favourite employment. Every night I was oppressed by a slow fever, and I became nervous to a most painful degree; the fall of a leaf startled me, and I shunned my fellow creatures as if I had been guilty of a crime. Sometimes I grew alarmed at the wreck I perceived that I had become; the energy of my purpose alone sustained me: my labours would soon end, and I believed that exercise and amusement would then drive away incipient disease; and I promised myself both of these when my creation should be complete.

_{Mary Shelley (1823). Frankenstein: or, the Modern Prometheus, volume I, pp. 94–96. London: G. and W. B. Whittaker.}

In the first paragraph of chapter 4, the creature came to life in the early morning:

It was on a dreary night of November, that I beheld the accomplishment of my toils. With an anxiety that almost amounted to agony, I collected the instruments of life around me, that I might infuse a spark of being into the lifeless thing that lay at my feet. It was already one in the morning; the rain pattered dismally against the panes, and my candle was nearly burnt out, when by the glimmer of the half-extinguished light, I saw the dull yellow eye of the creature open; it breathed hard and a convulsive motion agitated its limbs.

_{Shelley, pp. 97–98.}

Frankenstein fled from the creature, and “wretchedly” passed the remainder of the night “in the courtyard”. Too afraid to return to his apartment, he wandered the streets, where he met Clerval descending from a coach. With Clerval’s moral support he plucked up the courage to brave the ascent, and found the creature was gone. The “nervous fever” which Frankenstein then succumbed to was presumably a continuation or worsening of the “slow fever” from chapter 3.

This seems to adequately explain the paragraph quoted at the head of the question. “Date” means “determine or specify the date or time of an event” (OED), and “the time that I dated my creation” means “the time, that I determined [to be] the date of my creation”, not (as wrongly interpreted in the question) “the time at which I determined the date of my creation”, so Frankenstein means that he was seized by the “nervous fever” on the same day that the creature came to life.

Normally one would use “dated to” if this were the meaning, but Shelley has structured the sentence with a relative clause (“the time that I dated my creation [to]”) and it is common to omit the preposition in a relative clause after “time” (and some other words, such as “manner” and “way”), for example,

the time that the unjust man doth thrive [in] (William Shakespeare, The Winter’s Tale IV.4)