If you started adoption proceedings. but have not yet been matched, can you receive adoption credit or must you have been matched/adopted a child to receive?

It depends.

 

The IRS says:

 

When to claim the credit

• Domestic adoptions: Claim expenses each year as you incur them, whether you finalize the adoption or identify an eligible child.
• Foreign adoptions: Claim expenses once the adoption is final. When it’s final, you can claim all eligible expenses you paid, including in past years.
• Adoption of children deemed by a state welfare agency as special needs or hard to place: Claim expenses when the adoption is final.

Please read this IRS document for more information.