@tanguatlay,
Using the possessive with ambulance is okay, T.
Here are some other ways to put it though I must tell you, to my mind, they still are a little strange. A siren is heard long before an ambulance arrives so though the grammar is fine, it does sound a wee bit odd. Why not cut 'arriving'?
1. Soon they heard the siren of an
arriving ambulance [arriving].
2. Soon they heard the wail/wails/wailing of the siren of an
arriving ambulance [arriving].
3. Soon they heard the wail/wails/wailing of an
arriving ambulance [arriving].