Since I'm slacking off, here's a straightforward, not at all optimized Go implementation:

  package main
  
  import (
      "bytes"
      "crypto/sha256"
      "encoding/hex"
      "fmt"
  )
  
  var (
      _chars = []byte("0123456789abcdef")
      _names = []string{"zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "a", "b", "c", "d", "e", "f"}
      _size  = len(_chars)
  )
  
  func main() {
      hexsum := make([]byte, 64)
      for i1 := 0; i1 < _size; i1++ {
          for i2 := 0; i2 < _size; i2++ {
              for i3 := 0; i3 < _size; i3++ {
                  for i4 := 0; i4 < _size; i4++ {
                      for i5 := 0; i5 < _size; i5++ {
                          for i6 := 0; i6 < _size; i6++ {
                              for i7 := 0; i7 < _size; i7++ {
                                  s := fmt.Sprintf("The SHA256 for this sentence begins with: %s, %s, %s, %s, %s, %s and %s.", _names[i1], _names[i2], _names[i3], _names[i4], _names[i5], _names[i6], _names[i7])
                                  sum := sha256.Sum256([]byte(s))
                                  hex.Encode(hexsum, sum[:])
                                  prefix := []byte{_chars[i1], _chars[i2], _chars[i3], _chars[i4], _chars[i5], _chars[i6], _chars[i7]}
                                  if bytes.HasPrefix(hexsum, prefix) {
                                      fmt.Printf("%s\n", s)
                                      fmt.Printf("%s\n", hexsum)
                                  }
                              }
                          }
                      }
                  }
              }
          }
      }
  }

Takes a few minutes on common consumer hardware. There's exactly one hit.

(Easiest optimization is wrapping the loop body in a goroutine. GOEXPERIMENT=loopvar really makes this nicer btw.)

The reply is obviously more interesting, need to come up with a lot of variations.