usually, if a yeshivish boy and girl “make their own shidduch”, it raises eyebrows, because people are skeptical that two frum adults who are of marriageable age could keep the non-shidduch-relationship appropriate.
there are going to be tons of differing opinions on this thread of what is considered appropriate, but in my view, I don’t see anything wrong with two people meeting and setting themselves up, or asking an outside party, in this case the boys mother, to do something about it to have them go out officially on a shidduch date. you can argue forevermore if its appropriate for frum singles to be working in mixed gender workplaces–that isn’t the point here.
if the couple are behaving in a mature, responsible, and appropriate fashion, I don’t see why it should be a problem. I’m sure there are plenty of excellent and yashar people on these boards, who belong to the yeshiva world, who have met their spouses without being formally introduced by a shadchan…….