"Avoir" is linked to the concept of possession, be it of a material object or something abstract. For instance, you can say :

J'ai un ballon
J'ai 8 ans

because both a ball and age are considered a possession in French.

As for your question, you're right, originally, " j'ai eu " meant "I've had something but not anymore".
But nowadays, when we use it without mentioning a specific date or period, it usually means something like " J'ai reçu "/"I obtained/received/...".
For instance,

J'ai eu une grosse opportunité.

usually means

I have a great opportunity.

Because nothing implies that I don't have it anymore.
BUT,

J'ai eu une grosse opportunité à l'époque mais...

usually means

I have had a great opportunity at the time but...

At the time implies not anymore.

As you can see this is just for conveniance that we say it that way. Unless you see a specific period of time, "j'ai eu" is to be understood "j'ai reçu/ j'ai eu depuis".

"Avoir" is linked to the concept of possession, be it of a material object or something abstract. For instance, you can say :

J'ai un ballon
J'ai 8 ans

because both a ball and age are considered a possession in French.

As for your question, you're right, originally, j'ai eu meant "I had something but not anymore".
But nowadays, when we use it without mentioning a specific date or period, it usually means something like " J'ai reçu "/"I obtained/received/...".
For instance,

J'ai eu une grosse opportunité.

usually means

I have a great opportunity.

Because nothing implies that I don't have it anymore.
BUT,

J'ai eu une grosse opportunité à l'époque mais...

usually means

I have had a great opportunity at the time but...

At the time implies not anymore.

As you can see this is just for conveniance that we say it that way. Unless you see a specific period of time, "j'ai eu" is to be understood "j'ai reçu/ j'ai eu depuis".