Unfortunately not. The following rule states that you have to provide 10 days notice. I would send the notice out now for 10 days later and then contact her attorney to see if he will agree to allow the deposition to go forward. If not, then you may need to motion the court to allow you to take the deposition after the discovery deadline.
2025.270. (a) An oral deposition shall be scheduled for a date at
least 10 days after service of the deposition notice.
(b) Notwithstanding subdivision (a), in an unlawful detainer
action or other proceeding under Chapter 4 (commencing with Section
1159) of Title
3 of Part 3, an oral deposition shall be scheduled for
a date at least five days after service of the deposition notice,
but not later than five days before trial.
(c) Notwithstanding subdivisions (a) and (b), if, as defined in
Section 1985.3 or 1985.6, the party giving notice of the deposition
is a subpoenaing party, and the deponent is a witness commanded by a
to produce personal records of a consumer or
employment records of an employee
, the deposition shall be scheduled
for a date at least 20 days after issuance of that subpoena.
(d) On motion or ex parte application of any party or deponent,
for good cause shown, the court may shorten or extend the time for
scheduling a deposition, or may stay its taking until the
determination of a motion for a protective order under Section