On a newly strung instrument, or after a complete restring, pitch goes through an unsettled period. This is the normal process of string tension releasing and rebalancing.
The typical sign is that a string you have just tuned drops again quite soon, so it needs repeated small adjustments. New strings are especially prone to this, and it usually takes several playing sessions and retunings before they settle.
When stringing, increase tension in stages rather than pulling straight up to pitch. Bringing the string up over several passes, with an interval in between, lowers the risk of breakage and helps the tension release evenly.
A bridge shifting slightly during this period is also normal. A quick check of bridge positions before you play avoids surprises in the middle of a piece.
Changes in temperature and humidity lengthen the settling period. For the first while, it is best to keep a new instrument in a position where the environment stays relatively stable.