A word ending with a consonant followed by a word starting with a vowel is necessary but not sufficient for a liaison.
This rules out any liaison in:
Je suis très sociable. Neither the final s of suis, nor the final s of très is pronounced.
That doesn't mean final consonants are never pronounced in French. There are many words where they are, but this is unrelated to your question.
A potential liaison belongs to one of three groups:
- Mandatory liaisons. Not doing them is considered a mistake whatever the language register.
Les avions (the planes). Always pronounced with a liaison, no exception.
Je suis très optimiste. Liaison may be missed in colloquial relaxed French, depending on the speaker.
- Optional liaisons. These are more often realized in formal than in colloquial speech.
This group is the larger one:
Je suis une personne. My impression is that a liaison is often not realized.
- Forbidden ones. Realizing such a liaison is considered a mistake.
Le président autrichien.
Note that what group a liaison belongs to is not set in stone. There have been changes in the past and there are a few ongoing ones.
For example Wikipedia states the liaison after très is optional but in other sources, e.g. BDL and FLE, it is mandatory.
Finally, note that semi-vowels are definitely compatible with liaisons, e.g.:
/j/ Dans tes yeux. (mandatory liaison)
/ɥ/ Une sauce sans huile. (mandatory liaison)
/w/ Il respire avec ses ouïes (mandatory liaison)
As usual, there are exceptions:
Les oui et les non (forbidden liaison1)
Also, note that an h can influence the liaison, depending on whether its an aspirated h ("h aspiré") or not. Both are silent, but the aspirated h prevents the liaison. Normal rules apply if the h is not aspirated.
Des histoires (not aspirated, liaison)
Des hiboux (aspirated, no liaison)
You can find the complete list of words with an aspirated h on the wikipedia page.
1 Oui behaves exactly as if it had started with an aspirated H: "Houi"