We open the door at Shfoch chamatcha. I have heard that it is to invite Eliyahu, or to show a lack of worry on a leil shimurim. But would it be acceptable to open the door before ha lachma anya, when we invite people to join us? This has (AFAIK) not developed as a minhag but is there a reason not to? Should we not be making that offer sincerely?
(h/t my dad)
Your question boils down to two parts:
I have not stumbled upon any source that says that your door must be locked and closed for the entirety of the Seder.
This (excellent IMHO) question is addressed by Rav Yaakov Shapira (here), and he quotes Rav Kook in Olas Reiyah, that we obviously need to invite guests earlier on than Ha Lachma Anya, but we are just emphasizing a major point that we gained from Yetzias Mitzrayim, which was the Middah of Chessed:
הרב זצ'ל (עולת ראיה ח'ב עמ' רסב-רסד) מסביר שאין הכוונה באמירה להזמין אורח בפועל, את זה באמת צריך לעשות קודם לכן. אלא הכוונה להבליט את הנקודה המרכזית שקבלנו ביציאת מצרים, את מידת החסד.
Based on this, the reason why we don't open the door at this time is because we don't expect anyone to be coming at this point, we are just making this declaration about our earlier feelings, but not actually making an announcement to everyone to come in at this time. Therefore, there is no significant reason to open the door at this time any more than any other time.
Why we open for Shefoch Chamascha is (in my opinion) another, totally different question, which if I do not find on MY, I will ask.
This article (footnote 40) assumes that there used to be a minhag to open earlier.
[A recently published] manuscript from Rabbi Yuzpeh Shamash (1604-1678) of Worms...writes that it was the custom in Worms at the beginning of the seder to pour one extra cup of wine. Just as we say in the Haggadah, “Kol dichfin yesev v’yachul,” we prepare a glass for the guest who might come. This glass is called Kos Shel Eliyahu since this is the guest we await.
The author assumes that due to the connections between opening the door and Eliyahu (see the article for details), they must have opened the door at this point, when the cup of Eliyahu is poured.
So you see there might have existed such a minhag, but the minhag has developed to do it at the later part of the Seder. I would imagine it wouldn't be proper to do it earlier today, but I'm not a posek. I'm just saying it's called a seder (order) for a reason. It's best to do things in the order normally practiced.
