The Sefas Emes writes that the eight nights of Chanukah represent the tikun of the seven midos/sefiros that make up the natural world, and the eighth is the l’ma’lah min hateva of the supernatural.
Every person has a particular midah that is predominant -- some people tend towards chessed; other people tend towards din/geduvah, etc. -- but you can’t serve G-d with one midah alone and no single midah can exist alone. Every single midah needs to have within it elements and shades of all the others as well.
Let me give you a very bad analogy. You may like vanilla ice cream; I like chocolate. If you look at the ingredients on the containers, it turns out that most of what goes into either one is the same stuff. You can’t say, “I like vanilla ice cream so get that stuff that goes into the chocolate out of there.” You can’t make vanilla ice cream without those ingredients – you just need to accentuate the vanilla flavor so it is dominant. Same with the midos.
Now we can answer the Beis Yosef's question. Chanukah is not eight days of celebration; it's one celebration spread across eight days. If the ability for the menorah to be lit on night 2, 3,… 8, i.e. for the tikun of the midos going down the line for all eight days did not exist, then the menorah would not have been able to be lit on that first night either. Since every midah/day/candle requires the others to be present as well, the lighting of the candle on the first night presupposes and includes the potential for there to be a miraculous lighting on all the other nights as well.