Both the -Include and -Exclude parameters of provider cmdlets such as Get-ChildItem expect wildcard expressions that must match the names of the input items in full.

Thus, assuming the following:

• all files to match have a filename extension; to not enact this constraint, replace *.* with just * below.
• the base file name (the part before the extension) may either start with 4 digits, followed by arbitrary additional characters or comprise 4 digits only

you can use [0-9][0-9][0-9][0-9]*.*

In the context of your command:

Get-ChildItem -Recurse -File -LiteralPath D:testDigits -Include [0-9][0-9][0-9][0-9]*.* |
  Copy-Item -Destination D:transferTo

Note that you then do not need an -Exclude argument too.

Caveat:

• Due to your use of -Recurse, -Include and -Exclude do behave as expected, but in non-recursive processing they exhibit unintuitive behavior – see the bottom section of this answer.

If you need more sophisticated matching, use the approach suggested by Daniel:

• Use post-filtering, by way of the Where-Object cmdlet…

• … in combination with the regex-based -match operator

The – slower – (near-)equivalent of the above is:

Get-ChildItem -Recurse -File -LiteralPath D:testDigits |
  Where-Object Name -match '^[0-9]{4}'
  Copy-Item -Destination D:transferTo

Note:

• Unlike wildcard expressions, which match against the input string in full, regexes match substrings by default.

• The ^ in regex ^[0-9]{4} ensures that four ({4}) decimal digits ([0-9]) only match at the start of each input string.

  • As such, the above would also match extension-less files, unlike the [0-9][0-9][0-9][0-9]*.* wildcard expression, but like the [0-9][0-9][0-9][0-9]* variant.

    • Requiring a file-name extension would require a more complex regex, such as
      ^[0-9]{4}[^.]*..

  • Note: d is a commonly used shortcut class to refer to a digit, though, strictly speaking, it also matches what characters classified as digits in different scripts across the entire Unicode “alphabet”, which aren’t just the ASCII-range 0 to 9 characters, but also, for instance, ٠ (ARABIC-INDIC DIGIT ZERO, U+0660).
    However, in practice this is rarely a concern, and d is frequently used even when only 0 through 9 should be matched.

Performance considerations:

• A wildcard-based -Include / -Exclude outperforms a post-filtering solution based on Where-Object.

• The fastest – but limited – solution (which is not an option in the case at hand) is to use the -Filter parameter, because it filters at the provider source rather than retrieving all files first and then performing filtering.

  • The wildcard expressions accepted by -Filter (in the context of the FileSystem provider) are in essence limited to the * and ? constructs, along with obscure legacy behavior for backward-compatibility – see this answer.