Instead of this verse being about initial salvation, it is about what is necessary for the salvation of those whom Paul is addressing - those who clearly are already very Christian:
...your faith is proclaimed in all the world. - Romans 1:8
...we may be mutually encouraged by each other’s faith, both yours and mine. -Romans 1:12
...you are not under law but under grace. -Romans 6:14
...but you have received the Spirit of adoption as sons... -Romans 8:15
...I appeal to you, brothers, by our Lord Jesus Christ... -Romans 15:30
... “The word is near you, in your mouth and in your heart...” -Romans 10:8
It necessary for Christians to be saved to hold fast to what they believe:
1 I would remind you... of the gospel... 2 ...by which you are being saved, if you hold fast to the word ...-unless you believed in vain. -1 Corinthians 15:1-2
It is necessary for Christians who have died with Christ to confess him, for if you deny him he will deny you:
11 The saying is trustworthy, for:
If we have died with him, we will also live with him;
12 if we endure, we will also reign with him;
if we deny him, he also will deny us... -2 Timothy 2:11-12
Objection: Why, in Romans 10:9-10, does Paul talk about salvation in the future tense if he is talking about Christians? Aren’t we who are Christians already saved?
Yes, Paul considers that we already have been saved:
24 For in this hope we were saved... Romans 8:24
But, Paul also sees that we are in the process of being saved as we read above in 1 Corinthians 15:2
1 Now I would remind you, brothers, of the gospel I preached to you, which you received, in which you stand, 2 and by which you are being saved, if you hold fast to the word I preached to you—unless you believed in vain. -1 Corinthians 15:1-2
It is also the case that Paul sees our salvation as something that will happen on the Day of Judgement.
9 ...because we have now been declared righteous by his blood, we will be saved through him from God's wrath. Romans 5:9
11 For no one can lay a foundation other than that which is laid, which is Jesus Christ. 12 Now if anyone builds on the foundation with gold, silver, precious stones, wood, hay, straw— 13 each one’s work will become manifest, for the Day will disclose it, because it will be revealed by fire, and the fire will test what sort of work each one has done. 14 If the work that anyone has built on the foundation survives, he will receive a reward. 15 If anyone’s work is burned up, he will suffer loss, though he himself will be saved, but only as through fire. -1 Corinthians 3:11-15
This way of talking may be familiar to some who recognize the way Paul talks about the 'already, but not yet'...
In one passage, he says that we are already in the Kingdom:
13 He has delivered us from the domain of darkness and transferred us to the kingdom of his beloved Son, -Colossians 1:13
And in another that we have yet to enter the kingdom:
22 strengthening the souls of the disciples, encouraging them to continue in the faith, and saying that through many tribulations we must enter the kingdom of God. -Acts 14:22
Here’s one way to conceptualize the past, present, and future reality of our salvation:
If we will be saved in the future from the fire on the Day of Judgement, it will be because Jesus has saved us in the past through his death we have been united in. And as we await the coming Day, we are being saved presently if we are in Christ, believing in and confessing his name.
9 because, if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. 10 For with the heart one believes and is justified, and with the mouth one confesses and is saved. -Romans 10:9-10