[a speech another character made]という規定にしてしまった為、気付けば他薦応募で私たちが参加する事になっていた。 I think it should be something like "Due to [the speech], we became participants on the recommendation of others." The part I don't get is 気付けば. "We became participants on the recommendation of others if they noticed?" "If they were aware, others recommended us to become participants?" Thank you in advance!
気付けば is quoting definition: ふと注意を向けたらすでに事が起こっていた様子 or 意識がはじめてそこへ向いた様子 so, Before we aware of it/realized/noticed/Without our notice, we became participants on the recommendation of others, due to [certain regulation]?