It seems that there is very little evidence that the Steipler ever said this. However, the incident is quoted (from an unnamed source) in a Rabbi Frand d'var Torah.
Someone quoted an amazing story from the Steipler Gaon, related to this exact point. A person came to the Steipler and told him that he needed a blessing for his daughter. She was 27 years old and in need of a shidduch [marriage partner].
The Steipler asked him if it was his first daughter. The man replied that it was actually his third daughter. The Steipler then asked if when this daughter was born, her father made a Kiddush to celebrate her birth. The man admitted that although he had made celebrations when his first two daughters were born, by the third daughter, he, in fact, did not make a Kiddush to celebrate her birth.
The Steipler then advised him to go make a Kiddush for this 27 year old daughter. He said, "When you make a Kiddush, people come and give you brachos [blessings] for you and your daughter. They wish you Mazal Tov. They express all sorts of good wishes. Today, it is appropriate to wish fathers of newborn daughters a blessing that the father should find a shidduch easily for his daughter. People express such sentiments on such occasions. Twenty-seven years ago, you prevented your daughter from receiving those good wishes from the well-wishers you could have invited to your Kiddush. You never know from whence comes the bracha that will be heard in Heaven. The Almighty has all sorts of conduits for His blessing to take effect."
The Steipler continued, "Who knows, there might have been some neighbor or someone you met in shul who you could have invited by saying 'come, I'm making a Kiddush, I had a new daughter born this week'. He would have come in and taken a piece of cake and a little kuggle. He would have made a 'lechayim' and taken a shot of whiskey and then wished you: 'you should have an easy upbringing for her and you should find a good shidduch and be able to marry her off to a fine Talmid Chochom'. You could have responded "AMEN!" But you did not let that happen. You prevented your daughter from receiving all those blessings. Go now at age 27 and make a Kiddush for your daughter."
The end of the story is that the father did make the belated Kiddush and she soon thereafter became a Kallah.
This minhag is in direct opposition to quoted statements from the Steipler's son from reliable sources:
YGB - יג"ב: More Interesanter
Shticklach from R' Chaim Kanievski II
Rav Chaim Kanievski (son of the Steipler) says the famous legend about the fellow who had a hard time finding his daughter a shidduch, came to the Steipler, who asked him if he made a kiddush when the daughter was born, etc. is "sheker." And that he himself did not make kiddushim for most of his daughters.
My Belzer chevrusa (we learn "Sidduro shel Shabbos" together) told me, however, that they say over the same ma'aseh concerning the previous Belzer Rebbe. More tzugepast.
Does anyone have a better source for this? Is there any justification for the minhag (apart from being a nice thing to do - I have no problem, but is it a requirement?)
I have first hand evidence of women who did get married despite never having a kiddush made for them (which does not disprove anything, but makes it less serious).
Shlomo Pick is quite explicit on the subject:
From: Shlomo Pick
Date: Sun, 02 Jul 2000 13:31:18 +0200
Subject: Kiddush for Girls
shalom, Sorry to be late with this, but I have been involved in the simcha of marrying off my daughter and so this is a bit late. Recently I wrote concerning a kiddush for a daughter:
to that the following reply was sent:I heard the story from Rabbi Elchonon Halpern Shlita from London, who heard it first hand from the person who had the story with the Steipler!! How can one say that it NEVER happened just because HE didn't think it did! Does he know for a SURE? It doesn't matter if he is the Steipler's nephew!
i took up the challenge and and went back to the nephew, who re-reported that he had personally asked the steipler's son - rav chayim kanyevski - about the story. Rav Chayim dismissed it as "narishkeit" - foolishness. not to be taken lightly, i then went to Rav Chayim's son, Rav Shlomo Kanyevski, Rosh Yeshiva of Tiferet Zion in Bnei Brak. He confirmed that there was no family tradition to this. moreover, he reminded that he had not made a single kiddush for any daughter who had been born - afilu
pa'am achat! again he dismissed the story as narishkeit and suggested that his family tradition is the emesdic (truthful) one!
Anyone have anything else to add to this? I would love a more reliable source.