Classical Arabic does have Verb-Subject word order. But in this sentence, and sentences that show possession in general, the construction is "At [possessor] [possession]", rather than "[possessor] has [possession] like in English. So, instead of a verb, a preposition - the word عِنْد - is expressing the meaning of "have", and that indeed does come first before possessor.
hmmm, I have a slightly different opinion on this...slightly...
In Arabic in general a verb is not needed for a sentence - a verb is only needed when there is a change of state (vertical). When there is a description of a noun (horizontal), then the natural and go-to construction of a sentence is a nominal sentence (jumla ismiyya), where there is no change of state.
In MSA and especially in Classical Arabic, when describing a possession, there is no change of state - infact the best formation for possession is the 'idhafa' construction or 'mudhaaf and mudhaaf ilayh'
so that works as: [possession-possessor] as a phrase. The Arabic linguistic mind will not think in terms of 'Shady has a big garage' but in terms of 'Shady's big garage is ..... (added horizontal information, adjective)' or (Shady's big garage is ... (added vertical information, verb)' To form a sentence, more information is added about Shady's garage.
As an independent sentence however, if one wanted to describe the garage in a nominal sentence, then the possession would still resort to the idaafah construction. So the best way to do so in MSA would be:
الجراج الكبير جراج شادي
(The big garage is Shady's garage)
جراج شادي جراج كبير
(Shady's garage is a big garage)
جراج شادي كبير
(Shady's garage is big)
so 'Shady's garage' will remain in all cases, as the idafah. That is the difference between 'thinking in Arabic' and 'thinking in English'. A possession tends to not be worthwhile enough in the Arabic mind to form an independent sentence (so more information is needed - like 'what about Shady's garage?') as it would be in English.
Depending on which you want to emphasize on: the possession (the fact that it is Shady's) or the horizontal quality (the fact that it is big) you chose the sentence from the ones I stated as an example.
"At [possessor] [possession]" is a more dialectical construction. It is not good Arabic. The mindset of possession in MSA and classical Arabic, is idafah, or the possessive/attachment phrase.
And in all cases, this (كراج) is not the Arabic word for garage anyway... it is most definitely dialectical.
Merte18 - that's typically the case, but عِنْد is actually a preposition rather than a verb. Instead of a verb meaning "have" like in English or Spanish, Arabic uses a construction that means something like "At [possessor] [possession]. So instead of "Shadi has a big garage" the literal translation is "At Shadi big garage (or garage big)". In that case, the noun "garage" should have the -un nunation, being in the nominative case. However, the object of عِنْد should technically be in the dative/genitive, since this is the case that nouns take after a preposition. The vowel for this case is -i, or with nunation, -in.