No, the Soviets lost simply because we wasted more metal than they did.
Consider that just the Apollo programme had twenty one (21) launches in a span of about just 8 years before Apollo 11 landed the first men on the Moon.
Gemini had twelve (12) launches in a span of just 2 years, and Mercury had twenty six (26) launches in a span of just 4 years.
Contrast 4 launches of N1, 6 launches of Voskhod, and 13 launches of Vostok from records we know of.
Consider that just the Apollo programme had twenty one (21) launches in a span of about just 8 years before Apollo 11 landed the first men on the Moon.
Gemini had twelve (12) launches in a span of just 2 years, and Mercury had twenty six (26) launches in a span of just 4 years.
Contrast 4 launches of N1, 6 launches of Voskhod, and 13 launches of Vostok from records we know of.
If anything, Musk should waste more metal.