Well we don't have any surviving Norsemen of the time, no... but what we do have, are the brilliant minds of linguists and archaeologists [ myself included.
] and we can quite accurately reconstruct a system of Old Norse pronunciation based on various sources...
1) The rune carvings can shed light on to the phonemic qualities of spellings using the Roman alphabet.
2) Close examination of Old English, and Latin and other languages at the time can show how the Roman alphabet
would have been adapted for use with Old Norse.
3) Diachronistic study of Icelandic, Faroese and Norwegian can also give help in understanding how the pronunciation
developed which can show a lot about what it would have been originally.
I am confident in one particular system of pronunciation which is the result of 200 years of research. The pronunciation featured
in "A New Introduction To Old Norse I by Michael Barnes"
For those unfortunate enough not to own a copy, I may try and create a full guide, based on that and perhaps expanding on other points... I think it would be useful to have recorded pronunciations of words... I may try recording a few.
But it's not that much like modern Faroese or Icelandic unfortunately.