The transcription of "solely" is [ˈsəʊlli].
The fact that there are two "L" perplexes me.
Is it unnatural for you to pronounce "solely" with one "L"? (I mean: [ˈsəʊli])
the list of the dictionaries where the pronunciation of "solely" is [ˈsəʊlli]:
oxfordlearnersdictionaries.com
ldoceonline.com
cambridge.org
vocabulary.com says American speakers can omit one "L":
American English - [ˈsoʊ(l)li]
British English - [ˈsəʊlli]