Is there any way to accomplish this with cross platform .NET Core APIs
Yep!
X509Certificate2 cert;
using (ECDsa key = ECDsa.Create(ECCurve.NamedCurves.nistP256))
{
CertificateRequest request = new CertificateRequest(
"CN=Self-Signed ECDSA",
key,
HashAlgorithmName.SHA256);
request.CertificateExtensions.Add(
new X509KeyUsageExtension(X509KeyUsageFlags.DigitalSignature, critical: false));
request.CertificateExtensions.Add(
new X509BasicConstraintsExtension(false, false, 0, false));
// If it was for TLS, then Subject Alternative Names and
// Extended (Enhanced) Key Usages would also be useful.
DateTimeOffset start = DateTimeOffset.UtcNow;
cert = request.CreateSelfSigned(notBefore: start, notAfter: start.AddMonths(3));
}
// If you want to save a PFX or something, you can do so now.