No, there is not anything the president alone can do to stop a government shutdown by himself or herself.
To be able to stop or end a government shutdown, both the U.S. House of Representatives and the U.S. Senate must pass either full year appropriations bills or a temporary continuing resolution (CR).
Once Congress does pass the funding legislation for the government shutdown to end, the president must also sign it into law for government operations to resume.
The president cannot issue an executive order as executive orders cannot appropriate public money or bypass Congress's constitutional "power of the purse".
And the president also cannot independently draw funds from the Treasury or reallocate any money to restart the shut down federal agencies.
While the executive branch does have some discretion over which specific federal employees or activities are deemed "essential" and kept working under the Antideficiency Act, it also cannot reopen general government operations.
The president can however negotiate and lead and sign the bill.
The president can use political influence, negotiate with congressional leaders from both parties, and urge lawmakers to pass a budget or stop gap measure.
Then once a compromise is reached and approved by Congress, then the president is allowed and must sign the legislation to end the government shutdown.