# Java 8, 120 bytes

<!-- language-all: lang-java -->

 r->{var i=java.math.BigInteger.ONE;for(var t="";;i=i.add(i.ONE),t=i.toString(36))if(t.matches(r))System.out.println(t);}

Port of [*@l4m2*'s JavaScript answer](https://codegolf.stackexchange.com/a/272822/52210), so make sure to upvote that answer as well.

[Try it online.](https://tio.run/##LY8/C8IwEMV3P8XRKRHNIriEOggODtbBURzONK1X21SSsyDSz14T7HLcn8e732twwHVTPifTYghwQnLfBQA5tr5CY6FII8CFPbkajJgbL3Xcj4tYAiOTgQIc5JNf774DeqC8ic6qQ36oPdXH6Fdbr87FQVe9F0nCeZZpTTkpLEtB6SZXHEfu/0/EZislVYKTjXnYILyUl09g26n@zeoVRdw6wVKPk04or/e9jSgz0dBTCV1MNENfbyj/aZwyIsPlfZnNMcbpBw)

**Explanation:**

 r->{ // Method with String parameter and no return-type
 var i=java.math.BigInteger.ONE; // Loop-BigInteger `i`, starting at 1
 for(var t=""; // Temp-String `t`, starting empty
 // Loop indefinitely:
 ; // After every iteration:
 i=i.add(i.ONE), // Increase `i` by 1
 t=i.toString(36)) // Change `t` to `i` as base-36 string
 if(t.matches(r)) // If `t` fully† matches the input-regex:
 System.out.println(t);} // Print `t` with trailing newline

† Java's [String#matches](https://docs.oracle.com/javase/8/docs/api/java/lang/String.html#matches-java.lang.String-) implicitly adds a leading `^` and trailing `$` to match the regex on the entire String.