According to my knowledge in a marriage at-least following people should be present
- The Bride
- The Bride groom
- Bride's Father
- The Kazi
Is it possible that a marriage can be valid without presence or consent of Bride's Father and Kazi?
“There is no marriage except with a Walee, and two witnesses. The marriage is void otherwise. If they conflict, the Sultan is the Walee for whomever there is no Walee.”
(Abu Dawood: Nikah: 20; Tirmidhi: Nikah: 14; Ibn Majah: Nikah: 15; Ahmed b. Hanbal: Musned: 6/66.)
The above Hadith makes it clear that a Walee (Guardian) and two witnesses are must.
In Shi'i fiqh (ref.), yes it is valid if other terms are OK. For example for a virgin girl the permission of her father is needed but not his presence necessarily.
For marriage, witness is not needed but for divorce it is needed.
The minimum requirements for marriage:
1- The Brides guardian (Father, Uncle, ...)
2- The bride-groom (or a delegate)
3- Two witnesses
Note that Brides guardian is needed only if she is virgin. If she was married before, she can do it herself (doesn't need guardian).
The Wali, and two righteous/trustworthy witnesses must be present:
لا نكاح إلا بولي و شاهدي عدل
Marriage is not valid without the Wali and two righteous/trustworthy witnesses
Recorded by Ahmad, Ibn Hiban and others
It is both a requirement for the validity of the marriage for the Wali to give his permission for the marriage, as well as his presence. So no it is not possible at all. Furthermore I would like to mention that the consent of the bride is also necessary, but I do not believe that it is the answer for this question, so it can be for another question. And again I will mention that it is also a requirement for the presence of two witnesses for the validity of the marriage. Lastly I ask Allah's forgiveness of my mistakes, and that He guides us all.
Sources: Islamic online university Notes
Quran has set conditions for divorce so there have to be two witnesses:
فَإِذَا بَلَغْنَ أَجَلَهُنَّ فَأَمْسِكُوهُنَّ بِمَعْرُوفٍ أَوْ فَارِقُوهُنَّ بِمَعْرُوفٍ وَأَشْهِدُوا ذَوَيْ عَدْلٍ مِّنكُمْ وَأَقِيمُوا الشَّهَادَةَ لِلَّهِ ۚ ذَٰلِكُمْ يُوعَظُ بِهِ مَن كَانَ يُؤْمِنُ بِاللَّهِ وَالْيَوْمِ الْآخِرِ ۚ وَمَن يَتَّقِ اللَّهَ يَجْعَل لَّهُ مَخْرَجًا
(طلاق/2)
Then, when they have reached their term, retain them honourably, or part from them honourably. And call in to witness two men of equity from among yourselves; and perform the witnessing to God Himself. By this then is admonished whosoever believes in God and the Last Day. And whosoever fears God, He will appoint for him a way out,
There is not such a condition for marriage.