時期 and 時点: a period and a point used to assess a state
Compare a season for moving with seat availability at a stated time, keeping an assessment tied to its reference point.
When something happens
時期, read じき, identifies when something occurs or fits. 引っ越しの時期は春です。 says that the move is in spring.
忙しい時期を避けて旅行します。 says that travel is arranged to avoid a busy period. The focus is the character of a period rather than a state at one instant.
A reference point for an assessment
時点, read じてん, identifies the point at which a state is assessed. 午前九時の時点では、空席がありました。 says that seats were available as of nine a.m.
確認した時点では、まだ予約できました。 says that booking was still possible when it was checked. It does not automatically establish current availability.
Keeping timing separate from a dated assessment
開催時期は夏ですが、現時点では日付が未定です。 says that the event is in summer, but its date is undecided at present.
A 時点 need not be a clock reading: 決定した時点 uses the decision as a reference event. Distinguish when the information applies from whether it may later change.
Does 午前九時の時点では、空席がありました。 establish that seats are available now?
Show the answer and why
No. It gives past availability at nine a.m. The current state must be checked separately.