Flutter is pretty similar in that aspect to React.js.

There you would not try to access the element directly but rather update the state of the application. An approach similar to jQuery is not advisable.

There are multiple ways to communicate changes/updates to the widgets.

I would suggest checking out Fluttery youtube channel, there are plenty of suggestions on how to communicate events to widgets:
https://www.youtube.com/channel/UCtWyVkPpb8An90SNDTNF0Pg