First of all we can't know for sure Paul wrote Hebrews.
You can ask Jesus to help you see the truth in His words, even though Paul wrote as led by the Holy Spirit.
1 Corinthians 9:24 Know ye not that they which run in a race run all, but one receiveth the prize? So run, that ye may obtain. 25 And every man that striveth for the mastery is temperate in all things. Now they do it to obtain a corruptible crown; but we an incorruptible. 26 I therefore so run, not as uncertainly; so fight I, not as one that beateth the air: 27 But I keep under my body, and bring it into subjection: lest that by any means, when I have preached to others, I myself should be a castaway.
Hebrews 12:1Wherefore seeing we also are compassed about with so great a cloud of witnesses, let us lay aside every weight, and the sin which doth so easily beset us, and let us run with patience the race that is set before us, 2 Looking unto Jesus the author and finisher of our faith; who for the joy that was set before him endured the cross, despising the shame, and is set down at the right hand of the throne of God.
Hebrews 13:22 And I beseech you, brethren, suffer the word of exhortation: for I have written a letter unto you in few words. 23 Know ye that our brother Timothy is set at liberty; with whom, if he come shortly, I will see you. 24 Salute all them that have the rule over you, and all the saints. They of Italy salute you. 25 Grace be with you all. Amen.
Paul was a prisoner in Rome from which he had a lot of time to write letters or epistles to the churches.
The old testament saints and those in Christ from Jesus's and the twelve's earthly ministry are seeking the heavenly city in Revelation 21:2 the new Jerusalem
The firstfruit of the resurrection will be inheriting that city of God at the pre great tribulation rapture event for when after the great tribulation, the City of God will come down and dwell among men on earth. The saints growing up during the millennium reign will have access to that city of God to eat from the tree of life for the healing of the nations but do not live in that city of God because they live elsewhere from various places all over the world. I have read though that some will be born in that city from which expectant mothers may make it a point to visit that city for that blessing on that child being born, but as for living there, the child would obviously go home with his or her mother afterwards.