I have met several people who speak really good English yet they don’t pronounce the word support properly. This is one of the very few words whose pronunciation eludes even some very good speakers of English.
Many speakers put the stress on the first syllable which results in a different vowel sound, one used in a lot of words with a u, e.g. bus, cup, shut, Brussels, umbrella. The resulting pronunciation is thus */sʌpɔːt/, or */suhpawt/, whichever transcription you understand better.
So, why is this word pronounced differently? For starters, this word is stressed on the second syllable. How do I know that? Well, there is a rule that says: the second syllable of a two-syllable word is stressed if the second syllable contains a long vowel (e.g. balloon, racoon, support)*, a diphthong (two adjacent vowel sounds in the same syllable, e.g. apply, arrive) or if it ends with more than one consonant, e.g. attract, assist (this last rule doesn’t apply to most nouns).
Now that we’ve determined that the stress falls on the second syllable, we can conclude that the first syllable is a weak one. The most common weak vowel in English is the schwa /ə/.
It appears in the first syllable of all the words mentioned above:
balloon / bəˈluːn/, attract / əˈtrækt/, racoon / rəˈkuːn/, apply / əˈplaɪ/, arrive / əˈraɪv/ and of course support / səˈpɔːt/. You can listen to it here.
Unfortunately, you can never generalize phonetic rules in English because exceptions are plentiful. That’s why you should always consult a dictionary for support.
*Notice that in American English this word belongs to the ‘ends with more than one consonant” group since the r is pronounced: /səˈpɔrt/. For more on this: Rhoticity
Source and further reading: