From this paper: https://arxiv.org/pdf/2405.13500 :
Euclid takes its data in multiples of a so called reference observing sequence (ROS). Each of with consists of the following exposures:
An ROS field is composed of four dither pointings designed
to fill the detector gaps. For each dither, the same measurement sequence is executed. First comes a VIS $I_E$-band nominal science exposure of 566 s, with a concurrent NISP spectroscopic exposure of 574 s in one of the four red-grism orientations. These are followed by a sequence of three NISP images in the $J_E$, $H_E$, and $Y_E$ bands, each lasting 112 s. For the ERO programme, each dither also included an $I_E$ short-science exposure of 95 s simultaneously to the $Y_E$ exposure, yielding four such images per ROS;
So per ROS you get $(4\,\times\,566)+95 = 2359\,$s for the I-channel of the VIS instrument and $4\times112=448\,$s for the J, H & Y-channels of the NISP instrument. This is also nicely illustrated in Fig. 8 of this earlier paper https://arxiv.org/abs/2108.01201 :
(As this was written 3 yrs earlier, before the launch, I wouldn't worry about the few seconds difference.)
Those are then combines as RGB channels for the different images. The press release has some information on which channel, besides the I-channel, was used for which color in each image.
On top, for the early data release, each source gets between one and three of those ROSs, according to the table below. I leave the remaining math of adding up all those seconds as an exercise to the reader.
Another caveat would be that this is how observations where planned. Stuff like a solar flare can make some data unusable so for the precise exposure time of each image, one should consult also the papers mentioned in the table below.