Can I say "Neil Armstrong is the first man to walk on the Moon"?

Solution 1:

Using the present simple to talk about an event that took place in the past is called the narrative present, the historic/al present, or the dramatic present usage. See for example ThoughtCo_Nordquist. It is used to add tension to stories, drawing the audience in:

• (The door was ajar.

Matt Barratt draws his gun, aims at the figure standing on the chair, and shoots Bobby the Kid in his back.)

and in giving historical data, especially when listing events:

... ... ...

• 19 July. 1545 King Henry VIII looks on as his newly refitted flagship the Mary Rose sinks in the Solent, off England’s south coast, with the loss of 700 lives.
• 20 July. 1588 The Spanish Armada consisting of 130 warships set sail for England from Corunna, a day later than expected due to a storm.
• 21 July. 1969 The Eagle lands on the moon and US astronaut Neil Armstrong is the first man in history to walk on its powdery surface.
• 22 July. 1946 More than a year after the end of World War Two, bread is rationed in Britain. The shortage is blamed upon a poor harvest and drought.
• 23 July. 1940 The Local Defence Volunteers changes its name to the Home Guard. The one million-strong force, which includes many World War One veterans, is intended to form Britain’s last line of defence against the expected German invasion.
• 24 July. 1567 Mary Queen of Scots abdicates after defeat by the Protestants at Carberry Hill, near Musselburgh, East Lothian....

[Historic UK: Historic July] (note the inconsistency)

So, such a usage is certainly licensed. But as always, context is highly important. It would sound distinctly odd to choose the dramatic/historical present rather than past simple to state a past event in most contexts (including conversation and normal prose).