What Rashi is emphasizing is that we are to know and understand what the primary mission of the entire Congregation of Israel (כל עדת ישראל) is meant to be. Namely like it is written in Isaiah 49:3-7, which says:
וַיֹּ֥אמֶר לִ֖י עַבְדִּי־אָ֑תָּה יִשְׂרָאֵ֕ל אֲשֶׁר־בְּךָ֖ אֶתְפָּאָֽר׃
וַאֲנִ֤י אָמַ֙רְתִּי֙ לְרִ֣יק יָגַ֔עְתִּי לְתֹ֥הוּ וְהֶ֖בֶל כֹּחִ֣י כִלֵּ֑יתִי אָכֵן֙ מִשְׁפָּטִ֣י אֶת־יְהוָ֔ה וּפְעֻלָּתִ֖י אֶת־אֱלֹהָֽי׃
וְעַתָּ֣ה ׀ אָמַ֣ר יְהוָ֗ה יֹצְרִ֤י מִבֶּ֙טֶן֙ לְעֶ֣בֶד ל֔וֹ לְשׁוֹבֵ֤ב יַֽעֲקֹב֙ אֵלָ֔יו וְיִשְׂרָאֵ֖ל לא [ל֣וֹ] יֵאָסֵ֑ף וְאֶכָּבֵד֙ בְּעֵינֵ֣י יְהוָ֔ה וֵאלֹהַ֖י הָיָ֥ה עֻזִּֽי׃
וַיֹּ֗אמֶר נָקֵ֨ל מִֽהְיוֹתְךָ֥ לִי֙ עֶ֔בֶד לְהָקִים֙ אֶת־שִׁבְטֵ֣י יַעֲקֹ֔ב ונצירי [וּנְצוּרֵ֥י] יִשְׂרָאֵ֖ל לְהָשִׁ֑יב וּנְתַתִּ֙יךָ֙ לְא֣וֹר גּוֹיִ֔ם לִֽהְי֥וֹת יְשׁוּעָתִ֖י עַד־קְצֵ֥ה הָאָֽרֶץ׃ כֹּ֣ה אָֽמַר־יְהוָה֩ גֹּאֵ֨ל יִשְׂרָאֵ֜ל קְדוֹשׁ֗וֹ לִבְזֹה־נֶ֜פֶשׁ לִמְתָ֤עֵֽב גּוֹי֙ לְעֶ֣בֶד מֹשְׁלִ֔ים מְלָכִים֙ יִרְא֣וּ וָקָ֔מוּ שָׂרִ֖ים וְיִֽשְׁתַּחֲוּ֑וּ לְמַ֤עַן יְהוָה֙ אֲשֶׁ֣ר נֶאֱמָ֔ן קְדֹ֥שׁ יִשְׂרָאֵ֖ל וַיִּבְחָרֶֽךָּ׃
and (He) said to me, "You are My servant, Yisra᾽el, in whom I will be glorified."
Then I said, I have laboured in vain, I have spent my strength for nought, and in vain: yet surely my judgment is with the L-rd, and my reward with my G-d.
And now, says the Lord that formed me from the womb to be his servant to bring Ya῾acov back to him, that Yisra᾽el should be gathered to him, and I was honoured in the eyes of the L-rd, and my G-d was my strength.
And He said, "It is too slight a thing that you should be My servant to raise up the tribes of Ya῾acov, and to restore the preserved of Yisra᾽el: I will also give you as a light to the nations, that My salvation may be to the end of the earth."
Thus says the L-rd, the redeemer of Yisra᾽el, his Holy One, to him whom man despises, to him whom the nation abhors, to a servant of rulers, Kings shall see and arise, princes also shall prostrate themselves, because of the Lord who is faithful, and the Holy One of Yisra᾽el, who has chosen thee.
And this closing idea is precisely the scenario described in the Rashi to Bereshit 1:1 which you quote.
That if the nations of the world state "You are thieves! You conquered the land of the 7 nations!
When the nations express their abhorrence for Israel and how they despise them, we are to serve as a Light to the nations, serving Him to direct them back to proper service of G-d, the Creator of us all.
And this is exactly what Rashi directs our attention to, as is found in Tehillim, chapter 111:
וּמַה טַּעַם פָּתַח בִּבְרֵאשִׁית? מִשׁוּם כֹּחַ מַעֲשָׂיו הִגִּיד לְעַמּוֹ לָתֵת לָהֶם נַחֲלַת גּוֹיִם
But to truly understand the context of this single sentence, it is appropriate to look at Tehillim 111:1-9.
הַ֥לְלוּ יָ֨הּ ׀ אוֹדֶ֣ה יְ֭הוָה בְּכָל־לֵבָ֑ב בְּס֖וֹד יְשָׁרִ֣ים וְעֵדָֽה׃
גְּ֭דֹלִים מַעֲשֵׂ֣י יְהוָ֑ה דְּ֝רוּשִׁ֗ים לְכָל־חֶפְצֵיהֶֽם׃
הוֹד־וְהָדָ֥ר פָּֽעֳל֑וֹ וְ֝צִדְקָת֗וֹ עֹמֶ֥דֶת לָעַֽד׃
זֵ֣כֶר עָ֭שָׂה לְנִפְלְאֹתָ֑יו חַנּ֖וּן וְרַח֣וּם יְהוָֽה׃
טֶ֭רֶף נָתַ֣ן לִֽירֵאָ֑יו יִזְכֹּ֖ר לְעוֹלָ֣ם בְּרִיתֽוֹ׃
כֹּ֣חַ מַ֭עֲשָׂיו הִגִּ֣יד לְעַמּ֑וֹ לָתֵ֥ת לָ֝הֶ֗ם נַחֲלַ֥ת גּוֹיִֽם׃
מַעֲשֵׂ֣י יָ֭דָיו אֱמֶ֣ת וּמִשְׁפָּ֑ט נֶ֝אֱמָנִ֗ים כָּל־פִּקּוּדָֽיו׃
סְמוּכִ֣ים לָעַ֣ד לְעוֹלָ֑ם עֲ֝שׂוּיִ֗ם בֶּאֱמֶ֥ת וְיָשָֽׁר׃
פְּד֤וּת ׀ שָׁ֘לַ֤ח לְעַמּ֗וֹ צִוָּֽה־לְעוֹלָ֥ם בְּרִית֑וֹ קָד֖וֹשׁ וְנוֹרָ֣א שְׁמֽוֹ׃
Hallelujah. I praise the L-rd with all my heart in the assembled congregation of the Upright.
The works of the L-rd are great, within reach of all who desire them.
His deeds are splendid and glorious; His beneficence is everlasting;
He has won renown for His wonders. The L-rd is gracious and compassionate;
He gives food to those who fear Him; He is ever mindful of His covenant.
He revealed to His people His powerful works, in giving them the heritage of nations.
His handiwork is truth and justice; all His precepts are enduring,
well-founded for all eternity, wrought of truth and equity.
He sent redemption to His people; He ordained His covenant for all time; His name is holy and awesome.
There are two groups praising G-d, the Yasharim and the Congregation. The Yasharim refers to the children of Israel, those who are born Jews.
The Congregation is referring to the rest of the nation of Israel, those who convert (גרי-צדק) according to Jewish law and also to the righteous from among the nations, those who are referred to as the Children of Noach. They accept upon themselves to keep the seven commandments of Noach. And this entire group is described a little further as those who fear G-d.
It explains that G-d provides directly for the needs of those that fear Him. (It's worth pointing out that the word fear is related to the idea of movement and action, like is found in Tehillim 76:9. The emphasis being that we are expected to actually do what G-d commands us. Our action is the main idea.)
It then goes on to explain that G-d revealed His powerful actions, a reference to the acts of Creation, to His people, the people Israel, in order to give to them the inheritance of the nations. That this refers to the individuals from among the nations who upon hearing how G-d is the Creator of us all, will be drawn close to Israel including even wanting to become an actual part of the Jewish people through conversion according to G-d's law.
And as it concludes in Tehillim 111:9, Redemption was sent by G-d to His people, the people Israel, in order to connect (or command) His covenant to the world. That there is no place devoid of G-d.
And so what Rashi is saying is that we are to tell the world that there is one G-d, the Creator of us all, who supervises all things and in truth, justice and kindness, maintains and judges the entire world according to His will. He gives and takes according to what is upright in His view, not ours necessarily. And it is only in that context that we, His people Israel, at this time, have come into possession of the land of Israel again. Not because of our strength or greatness, but only because the Creator of us all has willed it so.
