Given the phrases that are in standard German, vg.:
Das Auto des Mannes.
Die Kirche des Gottes.
Could we use the following alternative word order?:
Das Mannes Auto.
Die Gottes Kirche.
The alternative word order exists, but you must keep the articles in genitive case:
Das Auto des Mannes = Des Mannes Auto.
Die Kirche des Gottes = Des Gottes Kirche.
I should add, that the form »das Auto des Mannes« is way more often used than »des Mannes Auto«. Later sounds old fashioned and is almost extinct. But it still is correct German. You better shouldn't use it actively, but it's good to know what it means when you hear or read it.
Yes, you can say
des Mannes Auto
but not
die Gottes Kirche
just
des Gottes Kirche
although that would mean the god's church i.e. the church of the god, not God's church.
Note that these second versions sound a little bit stilted, literary. You would probably not use them in normal day speech, nor in normal writing, except in some known expressions and sayings.
Yes, you can put the genitive part in front of the noun, however it then replaces the definite article. So it is
des Mannes Auto
and the article "des" belongs to "Mannes" while the whole part "des Mannes" determines "Auto".
In the same way
des Gottes Kirche.
Note that when referring to the Christian god in a Christian cultural context, "Gott" is usually not used with an article but more like a name, so in that case it would be
Gottes Kirche
or
die Kirche Gottes.