In speaking yes it can. Solda köpek. would mean 'the dog is on the left'.
But I don't actually recommend using the flexible word order for learners because you have to give the correct tonation so that it's understood easily. So it's not an easy job sometimes. Therefore Bir köpek solda. -> A dog is on the left. would be a safer choice to be understood more clearly.
Good morning hakimsopiak
"Solda bir köpek var." Translation: There is a dog on the left.
Solda - (adverb) - "to the left" & "on the left."
I have deleted the suffix -in from your answer.
Soldan - (adverb) - "to the left" - "on the left."
"Soldan bir köpek var." - To the left there is a dog.
Very good other (correct answer) I am saying your answer is correct.
Let's see if anyone disagrees.
If they do, they must explain why?
From me a like ^ & a lingot.
Have a very Happy New Year.
Why is there an apostrophe in İstanbul'da but not in solda?
Istanbul is a proper noun & like the genitive case suffixes an apostrophe is used before the suffix & your name too.
Seema'nın Türkçe gramer kitapları nerede? Where are Seema's Turkish grammar books?
Bugün evde bırakmış. Today she left them at home.
I know you have a good sense of humour. A subtle hint to revise your Turkish grammar.