Their call comes as part of National Adoption Week in Wales, which runs from October 19 to 25.
The National Adoption Service for Wales is marking the week with its Now is a Good Time campaign, sharing stories from families who have built their lives through adoption.
Councillor Eddie Williams, cabinet member for social care and health at Vale of Glamorgan Council, said: “Every child deserves the opportunity to grow up in a safe, stable and loving home where they feel supported and can reach their full potential.
“National Adoption Week is an important opportunity to raise awareness of adoption and encourage more people to consider whether they could make a lasting difference to a child’s life.
“There is no single profile for an adoptive parent, and people from a wide range of backgrounds and circumstances can offer a child the care, security and love they need.
“We would encourage anyone who has considered adoption to take that first step and find out more about the support available throughout the process and beyond.
“By helping more children find their permanent families, we can give them the best possible foundations for the future.”
Across Wales, initial enquiries to adopt have risen by 10 per cent over the past year, following a period of decline.
Despite this increase, the number of children waiting for adoption has also grown, up 11 per cent to a total of 310.
Vale, Valleys and Cardiff Adoption supports residents in the Vale of Glamorgan, Cardiff, Merthyr Tydfil, and Rhondda Cynon Taf.
One adoptive parent, Sam, who adopted his son 10 years ago as a single father, said:
He said: “I wasn’t sure I would be accepted as a single, gay adopter.
“I was nervous, it took a lot of courage to make that first phone call.
“There was no judgement at all, they made me feel really reassured.”
Eifion Burke, director of the National Adoption Service for Wales, said: “National Adoption Week provides a great opportunity to share and celebrate the joy created for many families in Wales through adoption.
“Adoption can bring unique challenges, but it is also an incredibly rewarding journey.
“We want people to know that no one adopts alone.
“A wide range of support is available to children and adoptive families across Wales, including therapeutic services, peer networks and community-based support, helping families to build strong, positive and lasting relationships.”
More information can be found at the Vale, Valleys and Cardiff Adoption website.