You mean "when the sun starts to swell," not "when earth starts to swell."
And this is a laughable concern. The Sun's main sequence is predicted to last another 4 billion years. That's more time than life has existed on Earth, about 16,000x as long as homo sapiens has existed.
If we're concerned with the survival something vaguely descended from homo sapiens in 4 billion years, there's little enough harm in taking another million years for our tech to get a little better before starting the project.
To nitpick, The End Of Life We Care About on Earth is only ~800 million years off[1], at the outside, barring some unforeseen catastrophe or some truly astounding planetary engineering. Still a long time, but no 4 billion years.
And this is a laughable concern. The Sun's main sequence is predicted to last another 4 billion years. That's more time than life has existed on Earth, about 16,000x as long as homo sapiens has existed.
If we're concerned with the survival something vaguely descended from homo sapiens in 4 billion years, there's little enough harm in taking another million years for our tech to get a little better before starting the project.