[verb (plain)] + と見るや [i-adj] + と見るや [na-adj] + だ + と見るや [noun] + だ + と見るや
と見るや follows a plain-form clause and means "the instant someone saw that", "no sooner had they judged that": a judgment is made and a quick, decisive action follows at once. It is literary, at home in novels and news reports.
The clause before と見るや is what someone has concluded, which need not be something seen with the eyes: すき隙がある, かちめ勝ち目がない. The second half is a past action by the same person, told as narrative, so it is never a request or your own plan.
In conversation, とわかると or とおもったら思ったら followed by すぐ says the same thing.