In Matthew 16:24 Jesus tells His disciples to pick up their crosses and follow Him. How would they have understood what He was saying?

In Matt 16:24 Jesus tells His disciples to pick up their crosses and follow Him. How would the apostles have understood what He was saying? He spoke these words before He was crucified, so the mention of a cross is a bit strange to me. The Greek word is "stauros" or "stauron" which means an upright stake. Jesus does tell the apostles in verse 16:21 what would shortly come to pass (His crucifixion) but the verse doesn't make any mention of crucifixion. We could surmise that Jesus told them that He would be crucified and the text just doesn't explicitly mention it, that could be a reasonable explanation, but what if He didn't give them those details? It creates a dilemma of sorts. I'd be interested in hearing how other people understand this passage.