Looking for a single word or phrase
Solution 1:
Just to confirm Dan Bron's response for future readers, the term 'leg up' is used in horse riding, where the fingers are laced together and the rider places their knee (or foot if they're really short/the horse is really tall) in the helper's interlocked hands. The helper then boosts the rider up as they swing their leg over the horse's back.
Solution 2:
Try giving someone a boost
Here, boost means helping someone by pushing or raising them from below.
Example sentences - Boost him through the window. He gave me a boost to help me climb the wall.